Hi everyone,

I just found an easy proof that the answer to this problem:

http://www.openproblemgarden.org/op/even_vs_odd_latin_squares

....is that the conjecture is false, assuming I understand it correctly.

According to my understanding, it is actually the case that for every positive integer m, the number of even Latin squares of order m and the number of odd Latin squares of order m are *the same*.

Maybe I don't understand what is meant by this language:

"since interchanging the first two rows has no effect on the signs of the rows, but flips the signs of all of the columns."

(??? -- why does flipping the signs matter?)

"the signs of all of the row and column permutations"

(Doesn't that just mean the products of all the signs in all of the cells in all of the selected rows or columns in the selected permutation?)

-Philip White (philipjwhite@yahoo.com)

On Wednesday, June 22, 2022 at 1:40:21 PM UTC-4, B.H. wrote:
> Hi everyone,
>
> I just found an easy proof that the answer to this problem:
>
> http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>
> ...is that the conjecture is false, assuming I understand it correctly.
>
> According to my understanding, it is actually the case that for every positive integer m, the number of even Latin squares of order m and the number of odd Latin squares of order m are *the same*.
>
> Maybe I don't understand what is meant by this language:
>
> "since interchanging the first two rows has no effect on the signs of the rows, but flips the signs of all of the columns."
>
> (??? -- why does flipping the signs matter?)
>
> "the signs of all of the row and column permutations"
>
> (Doesn't that just mean the products of all the signs in all of the cells in all of the selected rows or columns in the selected permutation?)
>
> -Philip White (philip...@yahoo.com)

Maybe the writer means "permutations that include permutations of both columns and rows," but I interpreted it as "permutation of either some rows of the square or of some columns of the square, but not both."

-Philip White (philipjwhite@yahoo.com)

On Wednesday, June 22, 2022 at 1:42:30 PM UTC-4, B.H. wrote:
> On Wednesday, June 22, 2022 at 1:40:21 PM UTC-4, B.H. wrote:
> > Hi everyone,
> >
> > I just found an easy proof that the answer to this problem:
> >
> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >
> > ...is that the conjecture is false, assuming I understand it correctly.
> >
> > According to my understanding, it is actually the case that for every positive integer m, the number of even Latin squares of order m and the number of odd Latin squares of order m are *the same*.
> >
> > Maybe I don't understand what is meant by this language:
> >
> > "since interchanging the first two rows has no effect on the signs of the rows, but flips the signs of all of the columns."
> >
> > (??? -- why does flipping the signs matter?)
> >
> > "the signs of all of the row and column permutations"
> >
> > (Doesn't that just mean the products of all the signs in all of the cells in all of the selected rows or columns in the selected permutation?)
> >
> > -Philip White (philip...@yahoo.com)
> Maybe the writer means "permutations that include permutations of both columns and rows," but I interpreted it as "permutation of either some rows of the square or of some columns of the square, but not both."
>
> -Philip White (philip...@yahoo.com)

Note, I considered the negative signs to be affixed to the pre-existing symbols, i.e., I don't consider 2 and -2 to be different symbols here.

"B.H." <xlt.pjw@gmail.com> writes:

> Hi everyone,
>
> I just found an easy proof that the answer to this problem:
>
> http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>
> ...is that the conjecture is false, assuming I understand it correctly.
>
> According to my understanding, it is actually the case that for every
> positive integer m, the number of even Latin squares of order m and
> the number of odd Latin squares of order m are *the same*.

There is one even latin square of order 1. What is the odd latin square
of order one? How could there possibly be such a thing?

The number of even and odd latin squares is known for small n and they
are (so far) all different.

--
Ben.

On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> "B.H." <xlt...@gmail.com> writes:
>
> > Hi everyone,
> >
> > I just found an easy proof that the answer to this problem:
> >
> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >
> > ...is that the conjecture is false, assuming I understand it correctly.
> >
> > According to my understanding, it is actually the case that for every
> > positive integer m, the number of even Latin squares of order m and
> > the number of odd Latin squares of order m are *the same*.
> There is one even latin square of order 1. What is the odd latin square
> of order one? How could there possibly be such a thing?
>
> The number of even and odd latin squares is known for small n and they
> are (so far) all different.
>
> --
> Ben.

Since there are infinitely many integers, I decided to count Latin squares by sign. That is, each Latin square cell is either a "1" if its sign is negative, or a "0" if its sign is positive.

The odd Latin square of order 1 is simply the square with one cell containing -1.

I resolved the conjecture for 0-1 matrices and neglected the possibility of a Latin square with a 0 in a cell. Technically, that would make the conjecture true, if 0 and/or -0 were included as cell entries. The problem was specified vaguely on the OPG website, and I tend to react in problem solutions to precise (or non-precise) specifications of problems; I sort of took the liberty of treating it as the 0-1 matrix problem since no particular set was specified and one could use the set Z - {0}, although admittedly I didn't say I was doing that--I just didn't consider the number 0.

Anyway, for my version, the solution is correct...if you included the number 0, then the conjecture would be provably true, according to the logic of my proof that I will not publish. Admittedly, I could have been a little more precise--it's not a journal article though or other "extremely serious publication," so I didn't put that much time into it.

-Philip White (philipjwhite@yahoo.com)

"B.H." <xlt.pjw@gmail.com> writes:

> On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes:
>>
>> > Hi everyone,
>> >
>> > I just found an easy proof that the answer to this problem:
>> >
>> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>> >
>> > ...is that the conjecture is false, assuming I understand it correctly.
>> >
>> > According to my understanding, it is actually the case that for every
>> > positive integer m, the number of even Latin squares of order m and
>> > the number of odd Latin squares of order m are *the same*.
>> There is one even latin square of order 1. What is the odd latin square
>> of order one? How could there possibly be such a thing?
>>
>> The number of even and odd latin squares is known for small n and they
>> are (so far) all different.
>>
>
> Since there are infinitely many integers, I decided to count Latin
> squares by sign. That is, each Latin square cell is either a "1" if
> its sign is negative, or a "0" if its sign is positive.
>
> The odd Latin square of order 1 is simply the square with one cell
> containing -1.
>
> I resolved the conjecture

So you were addressing some other conjecture of your own. If the terms
used in the page you linked to have their usual meanings, it's clear
that the number of even Latin squares of order m and the number of odd
Latin squares of order m can not possibly be the same.

Making this clear up-front would have been helpful.

--
Ben.

On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> "B.H." <xlt...@gmail.com> writes:
>
> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> >> "B.H." <xlt...@gmail.com> writes:
> >>
> >> > Hi everyone,
> >> >
> >> > I just found an easy proof that the answer to this problem:
> >> >
> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >> >
> >> > ...is that the conjecture is false, assuming I understand it correctly.
> >> >
> >> > According to my understanding, it is actually the case that for every
> >> > positive integer m, the number of even Latin squares of order m and
> >> > the number of odd Latin squares of order m are *the same*.
> >> There is one even latin square of order 1. What is the odd latin square
> >> of order one? How could there possibly be such a thing?
> >>
> >> The number of even and odd latin squares is known for small n and they
> >> are (so far) all different.
> >>
> >
> > Since there are infinitely many integers, I decided to count Latin
> > squares by sign. That is, each Latin square cell is either a "1" if
> > its sign is negative, or a "0" if its sign is positive.
> >
> > The odd Latin square of order 1 is simply the square with one cell
> > containing -1.
> >
> > I resolved the conjecture
> So you were addressing some other conjecture of your own.

It's close enough. The same proof logic resolves all versions of the conjecture, and the purpose is to understand the logic of the proof and what it can imply, not just to understand one single fact about Latin squares.

> If the terms
> used in the page you linked to have their usual meanings, it's clear
> that the number of even Latin squares of order m and the number of odd
> Latin squares of order m can not possibly be the same.
>

What are the usual meanings? The terms are vague. Whether or not you have a math degree, you might want to clarify yourself.

-Philip

> Making this clear up-front would have been helpful.
>
> --
> Ben.

"B.H." <xlt.pjw@gmail.com> writes:

> On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes:
>>
>> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
>> >> "B.H." <xlt...@gmail.com> writes:
>> >>
>> >> > Hi everyone,
>> >> >
>> >> > I just found an easy proof that the answer to this problem:
>> >> >
>> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>> >> >
>> >> > ...is that the conjecture is false, assuming I understand it correctly.
>> >> >
>> >> > According to my understanding, it is actually the case that for every
>> >> > positive integer m, the number of even Latin squares of order m and
>> >> > the number of odd Latin squares of order m are *the same*.
>> >> There is one even latin square of order 1. What is the odd latin square
>> >> of order one? How could there possibly be such a thing?
>> >>
>> >> The number of even and odd latin squares is known for small n and they
>> >> are (so far) all different.
>> >>
>> >
>> > Since there are infinitely many integers, I decided to count Latin
>> > squares by sign. That is, each Latin square cell is either a "1" if
>> > its sign is negative, or a "0" if its sign is positive.
>> >
>> > The odd Latin square of order 1 is simply the square with one cell
>> > containing -1.
>> >
>> > I resolved the conjecture
>> So you were addressing some other conjecture of your own.
>
> It's close enough.

For what?

> The same proof logic resolves all versions of the conjecture, and the
> purpose is to understand the logic of the proof and what it can imply,
> not just to understand one single fact about Latin squares.

The version in the link you posted remains an open problem.

>> If the terms
>> used in the page you linked to have their usual meanings, it's clear
>> that the number of even Latin squares of order m and the number of odd
>> Latin squares of order m can not possibly be the same.
>
> What are the usual meanings? The terms are vague. Whether or not you
> have a math degree, you might want to clarify yourself.

You announced a solution without knowing what even and odd mean in the
context of Latin squares?

--
Ben.

On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
> "B.H." <xlt...@gmail.com> writes:
>
> > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> >> "B.H." <xlt...@gmail.com> writes:
> >>
> >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> >> >> "B.H." <xlt...@gmail.com> writes:
> >> >>
> >> >> > Hi everyone,
> >> >> >
> >> >> > I just found an easy proof that the answer to this problem:
> >> >> >
> >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >> >> >
> >> >> > ...is that the conjecture is false, assuming I understand it correctly.
> >> >> >
> >> >> > According to my understanding, it is actually the case that for every
> >> >> > positive integer m, the number of even Latin squares of order m and
> >> >> > the number of odd Latin squares of order m are *the same*.
> >> >> There is one even latin square of order 1. What is the odd latin square
> >> >> of order one? How could there possibly be such a thing?
> >> >>
> >> >> The number of even and odd latin squares is known for small n and they
> >> >> are (so far) all different.
> >> >>
> >> >
> >> > Since there are infinitely many integers, I decided to count Latin
> >> > squares by sign. That is, each Latin square cell is either a "1" if
> >> > its sign is negative, or a "0" if its sign is positive.
> >> >
> >> > The odd Latin square of order 1 is simply the square with one cell
> >> > containing -1.
> >> >
> >> > I resolved the conjecture
> >> So you were addressing some other conjecture of your own.
> >
> > It's close enough.
> For what?
> > The same proof logic resolves all versions of the conjecture, and the
> > purpose is to understand the logic of the proof and what it can imply,
> > not just to understand one single fact about Latin squares.
> The version in the link you posted remains an open problem.
> >> If the terms
> >> used in the page you linked to have their usual meanings, it's clear
> >> that the number of even Latin squares of order m and the number of odd
> >> Latin squares of order m can not possibly be the same.
> >
> > What are the usual meanings? The terms are vague. Whether or not you
> > have a math degree, you might want to clarify yourself.
> You announced a solution without knowing what even and odd mean in the
> context of Latin squares?
>
I had a look at the link and couldn't work out what the problem was.
Something to do with the product of the signs, but it doesn't actually
tell you which square is multiplied with which (It can't be simply
"multiply all squares" as the wording implies, because that's just a
parity problem.)
It's understandable that someone would have misunderstood the problem
if relying on that link.

On Friday, June 24, 2022 at 9:00:10 AM UTC+1, malcolm.ar...@gmail.com wrote:
> On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
> > "B.H." <xlt...@gmail.com> writes:
> >
> > > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> > >> "B.H." <xlt...@gmail.com> writes:
> > >>
> > >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> > >> >> "B.H." <xlt...@gmail.com> writes:
> > >> >>
> > >> >> > Hi everyone,
> > >> >> >
> > >> >> > I just found an easy proof that the answer to this problem:
> > >> >> >
> > >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> > >> >> >
> > >> >> > ...is that the conjecture is false, assuming I understand it correctly.
> > >> >> >
> > >> >> > According to my understanding, it is actually the case that for every
> > >> >> > positive integer m, the number of even Latin squares of order m and
> > >> >> > the number of odd Latin squares of order m are *the same*.
> > >> >> There is one even latin square of order 1. What is the odd latin square
> > >> >> of order one? How could there possibly be such a thing?
> > >> >>
> > >> >> The number of even and odd latin squares is known for small n and they
> > >> >> are (so far) all different.
> > >> >>
> > >> >
> > >> > Since there are infinitely many integers, I decided to count Latin
> > >> > squares by sign. That is, each Latin square cell is either a "1" if
> > >> > its sign is negative, or a "0" if its sign is positive.
> > >> >
> > >> > The odd Latin square of order 1 is simply the square with one cell
> > >> > containing -1.
> > >> >
> > >> > I resolved the conjecture
> > >> So you were addressing some other conjecture of your own.
> > >
> > > It's close enough.
> > For what?
> > > The same proof logic resolves all versions of the conjecture, and the
> > > purpose is to understand the logic of the proof and what it can imply,
> > > not just to understand one single fact about Latin squares.
> > The version in the link you posted remains an open problem.
> > >> If the terms
> > >> used in the page you linked to have their usual meanings, it's clear
> > >> that the number of even Latin squares of order m and the number of odd
> > >> Latin squares of order m can not possibly be the same.
> > >
> > > What are the usual meanings? The terms are vague. Whether or not you
> > > have a math degree, you might want to clarify yourself.
> > You announced a solution without knowing what even and odd mean in the
> > context of Latin squares?
> >
> I had a look at the link and couldn't work out what the problem was.
> Something to do with the product of the signs, but it doesn't actually
> tell you which square is multiplied with which (It can't be simply
> "multiply all squares" as the wording implies, because that's just a
> parity problem.)
> It's understandable that someone would have misunderstood the problem
> if relying on that link.

I too would be interested to know what the problem is about. I don't think I have ever heard of the "sign" of a permutation. If it simply means whether the permutation can be made up of an odd or even number of pair switches then the results don't seem consistent with those given on the page.

On Thursday, June 23, 2022 at 9:28:34 PM UTC-4, Ben Bacarisse wrote:
> "B.H." <xlt...@gmail.com> writes:
>
> > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> >> "B.H." <xlt...@gmail.com> writes:
> >>
> >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> >> >> "B.H." <xlt...@gmail.com> writes:
> >> >>
> >> >> > Hi everyone,
> >> >> >
> >> >> > I just found an easy proof that the answer to this problem:
> >> >> >
> >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >> >> >
> >> >> > ...is that the conjecture is false, assuming I understand it correctly.
> >> >> >
> >> >> > According to my understanding, it is actually the case that for every
> >> >> > positive integer m, the number of even Latin squares of order m and
> >> >> > the number of odd Latin squares of order m are *the same*.
> >> >> There is one even latin square of order 1. What is the odd latin square
> >> >> of order one? How could there possibly be such a thing?
> >> >>
> >> >> The number of even and odd latin squares is known for small n and they
> >> >> are (so far) all different.
> >> >>
> >> >
> >> > Since there are infinitely many integers, I decided to count Latin
> >> > squares by sign. That is, each Latin square cell is either a "1" if
> >> > its sign is negative, or a "0" if its sign is positive.
> >> >
> >> > The odd Latin square of order 1 is simply the square with one cell
> >> > containing -1.
> >> >
> >> > I resolved the conjecture
> >> So you were addressing some other conjecture of your own.
> >
> > It's close enough.
> For what?

It is close enough to provide a clear solution to whatever conjecture you likely think it is.

> > The same proof logic resolves all versions of the conjecture, and the
> > purpose is to understand the logic of the proof and what it can imply,
> > not just to understand one single fact about Latin squares.
> The version in the link you posted remains an open problem.

I disagree. The proof is useless, I might publish it if you would agree to acknowledge that it is correct and not just auto-smear me.

> >> If the terms
> >> used in the page you linked to have their usual meanings, it's clear
> >> that the number of even Latin squares of order m and the number of odd
> >> Latin squares of order m can not possibly be the same.
> >
> > What are the usual meanings? The terms are vague. Whether or not you
> > have a math degree, you might want to clarify yourself.
> You announced a solution without knowing what even and odd mean in the
> context of Latin squares?

I don't have time to read academic papers, I'm not being paid. I read the definitions on OPG and Wikipedia.

Do you know what they are? I stated my understanding, why do you think it's I who have some serious explaining to do, Dr. Bacarisse?

>
> --
> Ben.

At least you're getting some more attention paid to my threads.

-Philip White (philipjwhite@yahoo.com)

On Friday, June 24, 2022 at 7:50:34 AM UTC-4, Paul N wrote:
> On Friday, June 24, 2022 at 9:00:10 AM UTC+1, malcolm.ar...@gmail.com wrote:
> > On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
> > > "B.H." <xlt...@gmail.com> writes:
> > >
> > > > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> > > >> "B.H." <xlt...@gmail.com> writes:
> > > >>
> > > >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> > > >> >> "B.H." <xlt...@gmail.com> writes:
> > > >> >>
> > > >> >> > Hi everyone,
> > > >> >> >
> > > >> >> > I just found an easy proof that the answer to this problem:
> > > >> >> >
> > > >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> > > >> >> >
> > > >> >> > ...is that the conjecture is false, assuming I understand it correctly.
> > > >> >> >
> > > >> >> > According to my understanding, it is actually the case that for every
> > > >> >> > positive integer m, the number of even Latin squares of order m and
> > > >> >> > the number of odd Latin squares of order m are *the same*.
> > > >> >> There is one even latin square of order 1. What is the odd latin square
> > > >> >> of order one? How could there possibly be such a thing?
> > > >> >>
> > > >> >> The number of even and odd latin squares is known for small n and they
> > > >> >> are (so far) all different.
> > > >> >>
> > > >> >
> > > >> > Since there are infinitely many integers, I decided to count Latin
> > > >> > squares by sign. That is, each Latin square cell is either a "1" if
> > > >> > its sign is negative, or a "0" if its sign is positive.
> > > >> >
> > > >> > The odd Latin square of order 1 is simply the square with one cell
> > > >> > containing -1.
> > > >> >
> > > >> > I resolved the conjecture
> > > >> So you were addressing some other conjecture of your own.
> > > >
> > > > It's close enough.
> > > For what?
> > > > The same proof logic resolves all versions of the conjecture, and the
> > > > purpose is to understand the logic of the proof and what it can imply,
> > > > not just to understand one single fact about Latin squares.
> > > The version in the link you posted remains an open problem.
> > > >> If the terms
> > > >> used in the page you linked to have their usual meanings, it's clear
> > > >> that the number of even Latin squares of order m and the number of odd
> > > >> Latin squares of order m can not possibly be the same.
> > > >
> > > > What are the usual meanings? The terms are vague. Whether or not you
> > > > have a math degree, you might want to clarify yourself.
> > > You announced a solution without knowing what even and odd mean in the
> > > context of Latin squares?
> > >
> > I had a look at the link and couldn't work out what the problem was.
> > Something to do with the product of the signs, but it doesn't actually
> > tell you which square is multiplied with which (It can't be simply
> > "multiply all squares" as the wording implies, because that's just a
> > parity problem.)
> > It's understandable that someone would have misunderstood the problem
> > if relying on that link.
> I too would be interested to know what the problem is about. I don't think I have ever heard of the "sign" of a permutation. If it simply means whether the permutation can be made up of an odd or even number of pair switches then the results don't seem consistent with those given on the page.

The permutation is a selection of items. If you've studied basic combinatorics, you might know about permutations (order matters, there's a formula) and combinations (order does not matter, there's a formula for that too).

The problem is easy for me to prove...would anyone else care to post the proof? You could just post it for the neglected 0's version, which is false, which implies that the un-neglected 0's version is true.

Let's see if Ben Bacarisse will admit he doesn't understand the proof of the problem, assuming that he indeed does not understand it, since he's not a mathematician.

-Philip White (philipjwhite@yahoo.com)

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes:
>>
>> > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
>> >> "B.H." <xlt...@gmail.com> writes:
>> >>
>> >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
>> >> >> "B.H." <xlt...@gmail.com> writes:
>> >> >>
>> >> >> > Hi everyone,
>> >> >> >
>> >> >> > I just found an easy proof that the answer to this problem:
>> >> >> >
>> >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>> >> >> >
>> >> >> > ...is that the conjecture is false, assuming I understand it correctly.
>> >> >> >
>> >> >> > According to my understanding, it is actually the case that for every
>> >> >> > positive integer m, the number of even Latin squares of order m and
>> >> >> > the number of odd Latin squares of order m are *the same*.
>> >> >> There is one even latin square of order 1. What is the odd latin square
>> >> >> of order one? How could there possibly be such a thing?
>> >> >>
>> >> >> The number of even and odd latin squares is known for small n and they
>> >> >> are (so far) all different.
>> >> >>
>> >> >
>> >> > Since there are infinitely many integers, I decided to count Latin
>> >> > squares by sign. That is, each Latin square cell is either a "1" if
>> >> > its sign is negative, or a "0" if its sign is positive.
>> >> >
>> >> > The odd Latin square of order 1 is simply the square with one cell
>> >> > containing -1.
>> >> >
>> >> > I resolved the conjecture
>> >> So you were addressing some other conjecture of your own.
>> >
>> > It's close enough.
>> For what?
>> > The same proof logic resolves all versions of the conjecture, and the
>> > purpose is to understand the logic of the proof and what it can imply,
>> > not just to understand one single fact about Latin squares.
>> The version in the link you posted remains an open problem.
>> >> If the terms
>> >> used in the page you linked to have their usual meanings, it's clear
>> >> that the number of even Latin squares of order m and the number of odd
>> >> Latin squares of order m can not possibly be the same.
>> >
>> > What are the usual meanings? The terms are vague. Whether or not you
>> > have a math degree, you might want to clarify yourself.
>> You announced a solution without knowing what even and odd mean in the
>> context of Latin squares?
>>
> I had a look at the link and couldn't work out what the problem was.
> Something to do with the product of the signs, but it doesn't actually
> tell you which square is multiplied with which (It can't be simply
> "multiply all squares" as the wording implies, because that's just a
> parity problem.)
> It's understandable that someone would have misunderstood the problem
> if relying on that link.

Sure. I would hope, though, that someone tackling a hard open problem
would make sure they know what the terms mean ahead of time. A lot of
effort could be wasted otherwise.

For reference... Permutations are even or odd depending whether they
can be factored into an even or an odd number of swaps.

Now let s(p) = 1 if p is an even permutation and -1 is p is an odd
permutation. The parity of a Latin square, L, is given by

S(L) = (Product{k=1,n} s(r_k)) . (Product{k=1,n} s(c_k))

where r_k and c_k are the permutations present in the kth row and kth
column of L. Like s(p), S(L) is either 1 or -1 indicating even and odd
parity respectively.

--
Ben.

Paul N <gw7rib@aol.com> writes:

> On Friday, June 24, 2022 at 9:00:10 AM UTC+1, malcolm.ar...@gmail.com wrote:
>> On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
>> > "B.H." <xlt...@gmail.com> writes:
>> >
>> > > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
>> > >> "B.H." <xlt...@gmail.com> writes:
>> > >>
>> > >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
>> > >> >> "B.H." <xlt...@gmail.com> writes:
>> > >> >>
>> > >> >> > Hi everyone,
>> > >> >> >
>> > >> >> > I just found an easy proof that the answer to this problem:
>> > >> >> >
>> > >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>> > >> >> >
>> > >> >> > ...is that the conjecture is false, assuming I understand it correctly.
>> > >> >> >
>> > >> >> > According to my understanding, it is actually the case that for every
>> > >> >> > positive integer m, the number of even Latin squares of order m and
>> > >> >> > the number of odd Latin squares of order m are *the same*.
>> > >> >> There is one even latin square of order 1. What is the odd latin square
>> > >> >> of order one? How could there possibly be such a thing?
>> > >> >>
>> > >> >> The number of even and odd latin squares is known for small n and they
>> > >> >> are (so far) all different.
>> > >> >>
>> > >> >
>> > >> > Since there are infinitely many integers, I decided to count Latin
>> > >> > squares by sign. That is, each Latin square cell is either a "1" if
>> > >> > its sign is negative, or a "0" if its sign is positive.
>> > >> >
>> > >> > The odd Latin square of order 1 is simply the square with one cell
>> > >> > containing -1.
>> > >> >
>> > >> > I resolved the conjecture
>> > >> So you were addressing some other conjecture of your own.
>> > >
>> > > It's close enough.
>> > For what?
>> > > The same proof logic resolves all versions of the conjecture, and the
>> > > purpose is to understand the logic of the proof and what it can imply,
>> > > not just to understand one single fact about Latin squares.
>> > The version in the link you posted remains an open problem.
>> > >> If the terms
>> > >> used in the page you linked to have their usual meanings, it's clear
>> > >> that the number of even Latin squares of order m and the number of odd
>> > >> Latin squares of order m can not possibly be the same.
>> > >
>> > > What are the usual meanings? The terms are vague. Whether or not you
>> > > have a math degree, you might want to clarify yourself.
>> > You announced a solution without knowing what even and odd mean in the
>> > context of Latin squares?
>> >
>> I had a look at the link and couldn't work out what the problem was.
>> Something to do with the product of the signs, but it doesn't actually
>> tell you which square is multiplied with which (It can't be simply
>> "multiply all squares" as the wording implies, because that's just a
>> parity problem.)
>> It's understandable that someone would have misunderstood the problem
>> if relying on that link.
>
> I too would be interested to know what the problem is about. I don't
> think I have ever heard of the "sign" of a permutation.

It's common, when dealing with parity, to make even/odd to 1/-1. That
way parities can be combined with multiplication, just as permutations
can be factored and multiplied.

> If it simply
> means whether the permutation can be made up of an odd or even number
> of pair switches then the results don't seem consistent with those
> given on the page.

See my answer to MM on what the problem is about. Do you still see an
inconsistency? If so, maybe someone here can help of you explain what
you think is inconsistent.

--
Ben.

"B.H." <xlt.pjw@gmail.com> writes:

> On Thursday, June 23, 2022 at 9:28:34 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes:
>>
>> > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
>> >> "B.H." <xlt...@gmail.com> writes:
>> >>
>> >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
>> >> >> "B.H." <xlt...@gmail.com> writes:
>> >> >>
>> >> >> > Hi everyone,
>> >> >> >
>> >> >> > I just found an easy proof that the answer to this problem:
>> >> >> >
>> >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
>> >> >> >
>> >> >> > ...is that the conjecture is false, assuming I understand it correctly.
>> >> >> >
>> >> >> > According to my understanding, it is actually the case that for every
>> >> >> > positive integer m, the number of even Latin squares of order m and
>> >> >> > the number of odd Latin squares of order m are *the same*.
>> >> >> There is one even latin square of order 1. What is the odd latin square
>> >> >> of order one? How could there possibly be such a thing?
>> >> >>
>> >> >> The number of even and odd latin squares is known for small n and they
>> >> >> are (so far) all different.
>> >> >>
>> >> >
>> >> > Since there are infinitely many integers, I decided to count Latin
>> >> > squares by sign. That is, each Latin square cell is either a "1" if
>> >> > its sign is negative, or a "0" if its sign is positive.
>> >> >
>> >> > The odd Latin square of order 1 is simply the square with one cell
>> >> > containing -1.
>> >> >
>> >> > I resolved the conjecture
>> >> So you were addressing some other conjecture of your own.
>> >
>> > It's close enough.
>> For what?
>
> It is close enough to provide a clear solution to whatever conjecture you likely think it is.
>
>> > The same proof logic resolves all versions of the conjecture, and the
>> > purpose is to understand the logic of the proof and what it can imply,
>> > not just to understand one single fact about Latin squares.
>> The version in the link you posted remains an open problem.
>
> I disagree.

So far there is no proof one way or the other. That makes it an open
problem.

What you posted about before was about another problem (which may or not
have been open at the time) based on what you interpreted even/odd as
meaning for Latin squares. It had to be about another problem, because
the number of even and odd Latin squares is know for small n.

> The proof is useless, I might publish it if you would agree to
> acknowledge that it is correct and not just auto-smear me.

I did not intend to smear you, automatically or otherwise.

And I have no wish to add to your worries. I will happily not read what
you write if that would be preferable for you. Please let me know.

>> You announced a solution without knowing what even and odd mean in the
>> context of Latin squares?
>
> I don't have time to read academic papers, I'm not being paid. I read
> the definitions on OPG and Wikipedia.
>
> Do you know what they are? I stated my understanding, why do you
> think it's I who have some serious explaining to do, Dr. Bacarisse?

I have posted a reply to Malcolm with what I think is the correct
meaning for odd and even in the context of Latin squares. (I do not
have a PhD -- I am plain Mr -- but I prefer the more chatty Ben).

--
Ben.

"B.H." <xlt.pjw@gmail.com> writes:

> Let's see if Ben Bacarisse will admit he doesn't understand the proof
> of the problem, assuming that he indeed does not understand it, since
> he's not a mathematician.

What is a mathematician? I may very well not be a mathematician, but I
am not sure how such a term is generally defined and I have no idea how
you define it.

I don't want to go into detail about what you wrote unless you ask
because I don't want to smear you again and I think pretty much any
criticism of you work is a smear in your opinion. But do say if you
want to know what I really think.

--
Ben.

On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:
> "B.H." <xlt...@gmail.com> writes:
>
> > Let's see if Ben Bacarisse will admit he doesn't understand the proof
> > of the problem, assuming that he indeed does not understand it, since
> > he's not a mathematician.
> What is a mathematician? I may very well not be a mathematician, but I
> am not sure how such a term is generally defined and I have no idea how
> you define it.
>

I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.

> I don't want to go into detail about what you wrote unless you ask
> because I don't want to smear you again and I think pretty much any
> criticism of you work is a smear in your opinion. But do say if you
> want to know what I really think.
>
> --
> Ben.

I don't invite you to smear me; I'm not sure any discussion of my work would be informed by an understanding of what a mathematical proof is.

Are you really an adult, representing the UK on the internet, or do we need to change those two parameters (adult, UK, to clarify for the frivolity quibblers) to describe you?

-Philip White

On 6/24/2022 3:04 PM, B.H. wrote:
> On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes:
>>
>>> Let's see if Ben Bacarisse will admit he doesn't understand the proof
>>> of the problem, assuming that he indeed does not understand it, since
>>> he's not a mathematician.
>> What is a mathematician? I may very well not be a mathematician, but I
>> am not sure how such a term is generally defined and I have no idea how
>> you define it.
>>
>
> I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.

So Paul Erdos wasn't a mathematician by your definition? In fact you
have ruled out virtually all of the Field Medal winners. Would you like
a second try?

>> I don't want to go into detail about what you wrote unless you ask
>> because I don't want to smear you again and I think pretty much any
>> criticism of you work is a smear in your opinion. But do say if you
>> want to know what I really think.
>>
>> --
>> Ben.
>
> I don't invite you to smear me; I'm not sure any discussion of my work would be informed by an understanding of what a mathematical proof is.
>
> Are you really an adult, representing the UK on the internet, or do we need to change those two parameters (adult, UK, to clarify for the frivolity quibblers) to describe you?
>
> -Philip White
--
Jeff Barnett

On Friday, June 24, 2022 at 9:17:25 PM UTC+1, Ben Bacarisse wrote:
> Paul N <gw7...@aol.com> writes:
>
> > On Friday, June 24, 2022 at 9:00:10 AM UTC+1, malcolm.ar...@gmail.com wrote:
> >> On Friday, 24 June 2022 at 02:28:34 UTC+1, Ben Bacarisse wrote:
> >> > "B.H." <xlt...@gmail.com> writes:
> >> >
> >> > > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote:
> >> > >> "B.H." <xlt...@gmail.com> writes:
> >> > >>
> >> > >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote:
> >> > >> >> "B.H." <xlt...@gmail.com> writes:
> >> > >> >>
> >> > >> >> > Hi everyone,
> >> > >> >> >
> >> > >> >> > I just found an easy proof that the answer to this problem:
> >> > >> >> >
> >> > >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares
> >> > >> >> >
> >> > >> >> > ...is that the conjecture is false, assuming I understand it correctly.
> >> > >> >> >
> >> > >> >> > According to my understanding, it is actually the case that for every
> >> > >> >> > positive integer m, the number of even Latin squares of order m and
> >> > >> >> > the number of odd Latin squares of order m are *the same*.
> >> > >> >> There is one even latin square of order 1. What is the odd latin square
> >> > >> >> of order one? How could there possibly be such a thing?
> >> > >> >>
> >> > >> >> The number of even and odd latin squares is known for small n and they
> >> > >> >> are (so far) all different.
> >> > >> >>
> >> > >> >
> >> > >> > Since there are infinitely many integers, I decided to count Latin
> >> > >> > squares by sign. That is, each Latin square cell is either a "1" if
> >> > >> > its sign is negative, or a "0" if its sign is positive.
> >> > >> >
> >> > >> > The odd Latin square of order 1 is simply the square with one cell
> >> > >> > containing -1.
> >> > >> >
> >> > >> > I resolved the conjecture
> >> > >> So you were addressing some other conjecture of your own.
> >> > >
> >> > > It's close enough.
> >> > For what?
> >> > > The same proof logic resolves all versions of the conjecture, and the
> >> > > purpose is to understand the logic of the proof and what it can imply,
> >> > > not just to understand one single fact about Latin squares.
> >> > The version in the link you posted remains an open problem.
> >> > >> If the terms
> >> > >> used in the page you linked to have their usual meanings, it's clear
> >> > >> that the number of even Latin squares of order m and the number of odd
> >> > >> Latin squares of order m can not possibly be the same.
> >> > >
> >> > > What are the usual meanings? The terms are vague. Whether or not you
> >> > > have a math degree, you might want to clarify yourself.
> >> > You announced a solution without knowing what even and odd mean in the
> >> > context of Latin squares?
> >> >
> >> I had a look at the link and couldn't work out what the problem was.
> >> Something to do with the product of the signs, but it doesn't actually
> >> tell you which square is multiplied with which (It can't be simply
> >> "multiply all squares" as the wording implies, because that's just a
> >> parity problem.)
> >> It's understandable that someone would have misunderstood the problem
> >> if relying on that link.
> >
> > I too would be interested to know what the problem is about. I don't
> > think I have ever heard of the "sign" of a permutation.
> It's common, when dealing with parity, to make even/odd to 1/-1. That
> way parities can be combined with multiplication, just as permutations
> can be factored and multiplied.
> > If it simply
> > means whether the permutation can be made up of an odd or even number
> > of pair switches then the results don't seem consistent with those
> > given on the page.
> See my answer to MM on what the problem is about. Do you still see an
> inconsistency? If so, maybe someone here can help of you explain what
> you think is inconsistent.

Hi Ben

Thanks for your help. I was mis-reading it, hence my mistake. A 2x2 Latin square has one row of (1 2) which is even and one of (2 1) which is odd so I thought the square as a whole was odd. In fact you multiply all the rows AND all the columns so it is actually even.

Paul.

On Saturday, June 25, 2022 at 1:07:00 AM UTC-4, Jeff Barnett wrote:
> On 6/24/2022 3:04 PM, B.H. wrote:
> > On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:
> >> "B.H." <xlt...@gmail.com> writes:
> >>
> >>> Let's see if Ben Bacarisse will admit he doesn't understand the proof
> >>> of the problem, assuming that he indeed does not understand it, since
> >>> he's not a mathematician.
> >> What is a mathematician? I may very well not be a mathematician, but I
> >> am not sure how such a term is generally defined and I have no idea how
> >> you define it.
> >>
> >
> > I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.
> So Paul Erdos wasn't a mathematician by your definition? In fact you
> have ruled out virtually all of the Field Medal winners. Would you like
> a second try?

You are very incorrect, do you even know what ZFC is? Stepping up to the plate to smear me should not be done at all, and it looks like you have no idea how math/ZFC work, so at least you are too unprepared for right-wing fascist operational activity to be taken too seriously.

-Philip White

> >> I don't want to go into detail about what you wrote unless you ask
> >> because I don't want to smear you again and I think pretty much any
> >> criticism of you work is a smear in your opinion. But do say if you
> >> want to know what I really think.
> >>
> >> --
> >> Ben.
> >
> > I don't invite you to smear me; I'm not sure any discussion of my work would be informed by an understanding of what a mathematical proof is.
> >
> > Are you really an adult, representing the UK on the internet, or do we need to change those two parameters (adult, UK, to clarify for the frivolity quibblers) to describe you?
> >
> > -Philip White
> --
> Jeff Barnett

On 6/25/2022 8:22 AM, B.H. wrote:
> On Saturday, June 25, 2022 at 1:07:00 AM UTC-4, Jeff Barnett wrote:
>> On 6/24/2022 3:04 PM, B.H. wrote:
>>> On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:
>>>> "B.H." <xlt...@gmail.com> writes:
>>>>
>>>>> Let's see if Ben Bacarisse will admit he doesn't understand the proof
>>>>> of the problem, assuming that he indeed does not understand it, since
>>>>> he's not a mathematician.
>>>> What is a mathematician? I may very well not be a mathematician, but I
>>>> am not sure how such a term is generally defined and I have no idea how
>>>> you define it.
>>>>
>>>
>>> I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.
>> So Paul Erdos wasn't a mathematician by your definition? In fact you
>> have ruled out virtually all of the Field Medal winners. Would you like
>> a second try?
>
> You are very incorrect, do you even know what ZFC is? Stepping up to the plate to smear me should not be done at all, and it looks like you have no idea how math/ZFC work, so at least you are too unprepared for right-wing fascist operational activity to be taken too seriously.

Of course I know what ZFC is. I also know that virtually the only
mathematicians that directly use (or publish) WFF-only proofs are the
ones who are doing technical work in foundations or logic; even these
folks avoid that level of detail as much as possible. Most proofs use a
lot of verbiage and analogies to established theorems to convince the
reader.

The various theories that most mathematicians work with usually claim
that there work could be traced back to ZFC but the demonstrations of
those claims are rarely made explicit and are usually based on the facts
that their theory is based on another theory ..... that is based on ZFC.
And in fact there are several groups who explicitly claim to /not/ be
using ZFC, e.g., the Intuitionists.

And why the nasty reply? Don't let your self proclaimed personality
issues get in the way of these discussions. In fact, there are many open
threads in this forum where you have made claims and others have asked
you to back them up. The general result is that you don't. (Which
doesn't mean you can't but strongly suggests it.)
--
Jeff Barnett

On Saturday, June 25, 2022 at 1:25:38 PM UTC-4, Jeff Barnett wrote:
> On 6/25/2022 8:22 AM, B.H. wrote:
> > On Saturday, June 25, 2022 at 1:07:00 AM UTC-4, Jeff Barnett wrote:
> >> On 6/24/2022 3:04 PM, B.H. wrote:
> >>> On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:
> >>>> "B.H." <xlt...@gmail.com> writes:
> >>>>
> >>>>> Let's see if Ben Bacarisse will admit he doesn't understand the proof
> >>>>> of the problem, assuming that he indeed does not understand it, since
> >>>>> he's not a mathematician.
> >>>> What is a mathematician? I may very well not be a mathematician, but I
> >>>> am not sure how such a term is generally defined and I have no idea how
> >>>> you define it.
> >>>>
> >>>
> >>> I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.
> >> So Paul Erdos wasn't a mathematician by your definition? In fact you
> >> have ruled out virtually all of the Field Medal winners. Would you like
> >> a second try?
> >
> > You are very incorrect, do you even know what ZFC is? Stepping up to the plate to smear me should not be done at all, and it looks like you have no idea how math/ZFC work, so at least you are too unprepared for right-wing fascist operational activity to be taken too seriously.
> Of course I know what ZFC is. I also know that virtually the only
> mathematicians that directly use (or publish) WFF-only proofs are the
> ones who are doing technical work in foundations or logic; even these
> folks avoid that level of detail as much as possible. Most proofs use a
> lot of verbiage and analogies to established theorems to convince the
> reader.
>
> The various theories that most mathematicians work with usually claim
> that there work could be traced back to ZFC but the demonstrations of
> those claims are rarely made explicit and are usually based on the facts
> that their theory is based on another theory ..... that is based on ZFC.
> And in fact there are several groups who explicitly claim to /not/ be
> using ZFC, e.g., the Intuitionists.
>

You are now claiming to understand the exact point I made that you said was incorrect, not too subtle.

> And why the nasty reply? Don't let your self proclaimed personality
> issues get in the way of these discussions. In fact, there are many open
> threads in this forum where you have made claims and others have asked
> you to back them up. The general result is that you don't. (Which
> doesn't mean you can't but strongly suggests it.)

Because you smeared me, and that makes me think you are a right-wing human-trafficking supporter who wants to kill me for being disabled. My nastiness pales in comparison to yours, you might want to not engage in speech designed to murder innocent people; conspiracy to commit murder is a felony too, if I'm not mistaken, and you might want to read up on the felony murder statute, too. That's right, I'm accusing you of a crime.

Your claim about people asking me to back up claims is false AFAIK. Can you point to such a post in this thread? I believe I've answered every serious debating point and beyond, that's in my interests.

You should steer clear of hate, defamation, and crime.

-Philip White (philipjwhite@yahoo.com)

> --
> Jeff Barnett

On 6/25/2022 3:06 PM, B.H. wrote:

> On Saturday, June 25, 2022 at 1:25:38 PM UTC-4, Jeff Barnett wrote:
>> On 6/25/2022 8:22 AM, B.H. wrote:
>>> On Saturday, June 25, 2022 at 1:07:00 AM UTC-4, Jeff Barnett wrote:
>>>> On 6/24/2022 3:04 PM, B.H. wrote:

| Your reply to Ben Asking you "What is a mathematician".
\ /
>>>>> I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.

| My reply to your reply.
\ /

>>>> So Paul Erdos wasn't a mathematician by your definition? In fact you
>>>> have ruled out virtually all of the Field Medal winners. Would you like
>>>> a second try?

| Your reply that includes presumptions that politics, bad grammar,
| and no facts are part of a mathematical debate or discussion.
\ /

>>> You are very incorrect, do you even know what ZFC is? Stepping up to the plate to smear me should not be done at all, and it looks like you have no idea how math/ZFC work, so at least you are too unprepared for right-wing fascist operational activity to be taken too seriously.

| My reply to your unwarranted attack and explaining what I mean.
\ /

>> Of course I know what ZFC is. I also know that virtually the only
>> mathematicians that directly use (or publish) WFF-only proofs are the
>> ones who are doing technical work in foundations or logic; even these
>> folks avoid that level of detail as much as possible. Most proofs use a
>> lot of verbiage and analogies to established theorems to convince the
>> reader.
>>
>> The various theories that most mathematicians work with usually claim
>> that there work could be traced back to ZFC but the demonstrations of
>> those claims are rarely made explicit and are usually based on the facts
>> that their theory is based on another theory ..... that is based on ZFC.
>> And in fact there are several groups who explicitly claim to /not/ be
>> using ZFC, e.g., the Intuitionists.
| You now go completely off the rails and don't address above points!
\ /

> You are now claiming to understand the exact point I made that you said was incorrect, not too subtle.

What points made above by you? I don't see any. None!

| Information seeking query to you.
\ /

>> And why the nasty reply? Don't let your self proclaimed personality
>> issues get in the way of these discussions. In fact, there are many open
>> threads in this forum where you have made claims and others have asked
>> you to back them up. The general result is that you don't. (Which
>> doesn't mean you can't but strongly suggests it.)

| Another no fact answer and more unwarranted abuse from you.
\ /

> Because you smeared me, and that makes me think you are a right-wing human-trafficking supporter who wants to kill me for being disabled. My nastiness pales in comparison to yours, you might want to not engage in speech designed to murder innocent people; conspiracy to commit murder is a felony too, if I'm not mistaken, and you might want to read up on the felony murder statute, too. That's right, I'm accusing you of a crime.
>
> Your claim about people asking me to back up claims is false AFAIK. Can you point to such a post in this thread? I believe I've answered every serious debating point and beyond, that's in my interests.
>
> You should steer clear of hate, defamation, and crime.

The quickest way to find examples is look for threads in this forum
started by you that include at least three articles that were not
written by you. I think in the laboratory this is called making titers
to enrich the density of examples.

So an actual way for you to make progress is to select a standard
refereed math journal that does not specialize in foundations or logic
and count the proportions of articles that present "formal/informal
arguments based arguments based on wfs and proofs from ZFC". I believe
for most such journals, the proportion of articles that contain any WFFs
used to make "complete" assertions will be less that fifteen percent and
the number of articles that mention ZFC, specifically any axiom of ZFC,
or talk about Choice will be less that one percent.

The reason that mathematicians well over a century ago were debating
foundations, particularly various choice axioms, and secondarily various
continuum hypotheses, was that these axioms and their implications were
not well understood. Those days are long past and mathematicians today
pay no more attention to foundational issues in their day to day work
than they did in the middle-late nineteenth century. That is to say that
they don't.

On a slightly different topic: Have you ever heard of a program called
Perry? Talking to you reminds me a lot of interacting with it. Just curious.
--
Jeff Barnett

"B.H." <xlt.pjw@gmail.com> writes:

> On Friday, June 24, 2022 at 4:38:27 PM UTC-4, Ben Bacarisse wrote:

>> I don't want to go into detail about what you wrote unless you ask
>> because I don't want to smear you again and I think pretty much any
>> criticism of you work is a smear in your opinion. But do say if you
>> want to know what I really think.
>
> I don't invite you to smear me; I'm not sure any discussion of my work
> would be informed by an understanding of what a mathematical proof is.

I rather hoped for some clear advice: if I spot another error in
something you post, would you rather I keep quiet about it? And if
you'd rather I pointed it out, how can I do that without offending you?

> Are you really an adult,

Yes.

> representing the UK on the internet,

No.

> or do we need to change those two parameters (adult, UK, to clarify
> for the frivolity quibblers) to describe you?

I am an adult living in the UK. I am not sure why that matters to you,
but that's the truth, for what it's worth.

--
Ben.

On Saturday, June 25, 2022 at 6:40:31 PM UTC-4, Jeff Barnett wrote:
> On 6/25/2022 3:06 PM, B.H. wrote:
>
>
> > On Saturday, June 25, 2022 at 1:25:38 PM UTC-4, Jeff Barnett wrote:
> >> On 6/25/2022 8:22 AM, B.H. wrote:
> >>> On Saturday, June 25, 2022 at 1:07:00 AM UTC-4, Jeff Barnett wrote:
> >>>> On 6/24/2022 3:04 PM, B.H. wrote:
> | Your reply to Ben Asking you "What is a mathematician".
> \ /
> >>>>> I would say: Someone who studies formal/informal arguments based on wfs and proofs from ZFC.
> | My reply to your reply.
> \ /

I will answer your ignorant comments one more time.

> >>>> So Paul Erdos wasn't a mathematician by your definition? In fact you
> >>>> have ruled out virtually all of the Field Medal winners. Would you like
> >>>> a second try?
> | Your reply that includes presumptions that politics, bad grammar,
> | and no facts are part of a mathematical debate or discussion.
> \ /

The grammar is perfect, learn sentence diagramming. I did in 7th grade. My facts presented or alluded to are always accurate.

> >>> You are very incorrect, do you even know what ZFC is? Stepping up to the plate to smear me should not be done at all, and it looks like you have no idea how math/ZFC work, so at least you are too unprepared for right-wing fascist operational activity to be taken too seriously.
> | My reply to your unwarranted attack and explaining what I mean.
> \ /
> >> Of course I know what ZFC is. I also know that virtually the only
> >> mathematicians that directly use (or publish) WFF-only proofs are the
> >> ones who are doing technical work in foundations or logic; even these
> >> folks avoid that level of detail as much as possible. Most proofs use a
> >> lot of verbiage and analogies to established theorems to convince the
> >> reader.
> >>
> >> The various theories that most mathematicians work with usually claim
> >> that there work could be traced back to ZFC but the demonstrations of
> >> those claims are rarely made explicit and are usually based on the facts
> >> that their theory is based on another theory ..... that is based on ZFC.
> >> And in fact there are several groups who explicitly claim to /not/ be
> >> using ZFC, e.g., the Intuitionists.
> | You now go completely off the rails and don't address above points!
> \ /

Why should I have to address every prima facie stupid thing you say to try to kill me? I answer the one or two least dumb things you say.

You are simply trying to have a ball wasting my time. I am trying to survive. You are about to be done wasting my time by challenging me to debates that could kill me if I lost, which I never do--readers with education know..

> > You are now claiming to understand the exact point I made that you said was incorrect, not too subtle.
> What points made above by you? I don't see any. None!
>

I'm not copying and pasting what I said for you.

> | Information seeking query to you.
> \ /
> >> And why the nasty reply? Don't let your self proclaimed personality
> >> issues get in the way of these discussions. In fact, there are many open
> >> threads in this forum where you have made claims and others have asked
> >> you to back them up. The general result is that you don't. (Which
> >> doesn't mean you can't but strongly suggests it.)
> | Another no fact answer and more unwarranted abuse from you.
> \ /

It's not abuse, you're trying to get me killed during an emergency. You are contributing to such efforts. Me letting you breeze by my assertions that you don't react to properly doesn't make audiences let you off the hook in their eyes.

> > Because you smeared me, and that makes me think you are a right-wing human-trafficking supporter who wants to kill me for being disabled. My nastiness pales in comparison to yours, you might want to not engage in speech designed to murder innocent people; conspiracy to commit murder is a felony too, if I'm not mistaken, and you might want to read up on the felony murder statute, too. That's right, I'm accusing you of a crime.
> >
> > Your claim about people asking me to back up claims is false AFAIK. Can you point to such a post in this thread? I believe I've answered every serious debating point and beyond, that's in my interests.
> >
> > You should steer clear of hate, defamation, and crime.
> The quickest way to find examples is look for threads in this forum
> started by you that include at least three articles that were not
> written by you. I think in the laboratory this is called making titers
> to enrich the density of examples.
>

So link to one. You already have used up your one more Philip-White-correspondence opportunity anyway, so it's too late for you.

> So an actual way for you to make progress is to select a standard
> refereed math journal that does not specialize in foundations or logic
> and count the proportions of articles that present "formal/informal
> arguments based arguments based on wfs and proofs from ZFC". I believe
> for most such journals, the proportion of articles that contain any WFFs
> used to make "complete" assertions will be less that fifteen percent and
> the number of articles that mention ZFC, specifically any axiom of ZFC,
> or talk about Choice will be less that one percent.
>

I know about journals. All mathematical arguments are informal versions of ZFC-writeable formal proofs, did you not know that?
> The reason that mathematicians well over a century ago were debating
> foundations, particularly various choice axioms, and secondarily various
> continuum hypotheses, was that these axioms and their implications were
> not well understood. Those days are long past and mathematicians today
> pay no more attention to foundational issues in their day to day work
> than they did in the middle-late nineteenth century. That is to say that
> they don't.
>

Yes, people understand foundations. Mathematical arguments can be reduced to foundational arguments based on the axioms and inference rules.
> On a slightly different topic: Have you ever heard of a program called
> Perry? Talking to you reminds me a lot of interacting with it. Just curious.
> --
> Jeff Barnett

No, I don't know your thing.

I'm done here, go away and stop bothering me. I am trying to survive and not be trapped here forever.

-Philip White (philipjwhite@yahoo.com)