On 11/15/2023 6:30 AM, Fritz Feldhase wrote:
> On Wednesday, November 15, 2023 at 3:21:19 PM UTC+1, FromTheRafters wrote:
>> After serious thinking Adam Polak wrote :
>>>
>>> this: 1
>>> this: 23/23
>>> this: 1.00
>>> this: 1.(0)
>>> are completely different objects,
>
> No, they aren't.
>
>> No, they are different symbols for the number one.
>
> Right.
>
> 1 = 23/23 = 1.00 = 1.(0)
>
> Funny guy, our Adam.

Afaict, Adam is a sock puppet...

On 11/15/2023 10:53 AM, Fritz Feldhase wrote:
> On Wednesday, November 15, 2023 at 7:11:51 PM UTC+1, FromTheRafters wrote:
>
>> I look forward to reading the arguments between WM and Adam Polak.
>
> Same, same. Crank fight! :-)

LOL!!!! Crippled Brain Fight!

https://youtu.be/PeWMwrdFBw0?t=79

On 11/15/2023 8:29 AM, Fritz Feldhase wrote:
> On Wednesday, November 15, 2023 at 10:11:00 AM UTC+1, Adam Polak wrote:
>>
>> Find the difference between the pictures:
>>
>> Pict No. 1: 1/2
>>
>> Pict No. 2: 0.5
>>
>>
>> I'm sure everyone can spot it.
>
> Sure.
>
> What we SEE, are two different "symbolic expressions" (consisting of characters).
>
>> the differences are noticeable at first glance.
>
> Indeed! In "1/2" we spot the characters "1", "/", and "2". While in "0.5" we spot the characters "0", "." and "5".
>
>> these are two different mathematical objects!
>
> Nope. "1/2" and "0.5" are two different "symbols" (names, terms) which denote (in certain mathematical contexts like, say, analysis) one and the same mathematical object, namely the rational number 1/5.
>
> Hence these symbols
>
>> can be used interchangeably
>
> (in certain mathematical contexts like, say, analysis).
>
> Hint: 1/2 = 0.5 (there).
>
> Same with
>
>> This: 0.0009999... and this: 0.000(9)
>
> Hint: 0.0009999... = 0.000(9) (there).
>
>> <nonsense deleted>

Afaict, Adam the King of Fools, is a sock puppet for the long dead Gabriel?

Chris M. Thomasson formulated the question :
> On 11/15/2023 8:29 AM, Fritz Feldhase wrote:
>> On Wednesday, November 15, 2023 at 10:11:00 AM UTC+1, Adam Polak wrote:
>>>
>>> Find the difference between the pictures:
>>>
>>> Pict No. 1: 1/2
>>>
>>> Pict No. 2: 0.5
>>>
>>>
>>> I'm sure everyone can spot it.
>>
>> Sure.
>>
>> What we SEE, are two different "symbolic expressions" (consisting of
>> characters).
>>
>>> the differences are noticeable at first glance.
>>
>> Indeed! In "1/2" we spot the characters "1", "/", and "2". While in "0.5"
>> we spot the characters "0", "." and "5".
>>
>>> these are two different mathematical objects!
>>
>> Nope. "1/2" and "0.5" are two different "symbols" (names, terms) which
>> denote (in certain mathematical contexts like, say, analysis) one and the
>> same mathematical object, namely the rational number 1/5.
>>
>> Hence these symbols
>>
>>> can be used interchangeably
>>
>> (in certain mathematical contexts like, say, analysis).
>>
>> Hint: 1/2 = 0.5 (there).
>>
>> Same with
>>
>>> This: 0.0009999... and this: 0.000(9)
>>
>> Hint: 0.0009999... = 0.000(9) (there).
>>
>>> <nonsense deleted>
>
> Afaict, Adam the King of Fools, is a sock puppet for the long dead Gabriel?

He died again?

On Wednesday, November 15, 2023 at 9:30:15 PM UTC+1, Chris M. Thomasson wrote:
> On 11/15/2023 1:08 AM, Adam Polak wrote:
> > "Task for children" :) Find the difference between the pictures:
> >
> > Pict No. 1: 1/2
> > Pict No. 2: 0.5
> >
> 1/2 0.5
>
> one half = one half
>
> Find the difference:
>
> .5 .25 * 2
>
> 1/2 (1/4)*2

How about this:

1/2 * 2 = 1

0.5 * 2 = 1

Hence 1/2 * 2 = 0.5 * 2.

Dividing both sides by 2 we get:

1/2 = 0.5

:-P

On 11/15/2023 12:56 PM, FromTheRafters wrote:
> Chris M. Thomasson formulated the question :
>> On 11/15/2023 8:29 AM, Fritz Feldhase wrote:
>>> On Wednesday, November 15, 2023 at 10:11:00 AM UTC+1, Adam Polak wrote:
>>>>
>>>> Find the difference between the pictures:
>>>>
>>>> Pict No. 1: 1/2
>>>>
>>>> Pict No. 2: 0.5
>>>>
>>>>
>>>> I'm sure everyone can spot it.
>>>
>>> Sure.
>>>
>>> What we SEE, are two different "symbolic expressions" (consisting of
>>> characters).
>>>
>>>> the differences are noticeable at first glance.
>>>
>>> Indeed! In "1/2" we spot the characters "1", "/", and "2". While in
>>> "0.5" we spot the characters "0", "." and "5".
>>>
>>>> these are two different mathematical objects!
>>>
>>> Nope. "1/2" and "0.5" are two different "symbols" (names, terms)
>>> which denote (in certain mathematical contexts like, say, analysis)
>>> one and the same mathematical object, namely the rational number 1/5.
>>>
>>> Hence these symbols
>>>
>>>> can be used interchangeably
>>>
>>> (in certain mathematical contexts like, say, analysis).
>>>
>>> Hint: 1/2 = 0.5 (there).
>>>
>>> Same with
>>>
>>>> This: 0.0009999... and this: 0.000(9)
>>>
>>> Hint: 0.0009999... =  0.000(9) (there).
>>>
>>>> <nonsense deleted>
>>
>> Afaict, Adam the King of Fools, is a sock puppet for the long dead
>> Gabriel?
>
> He died again?

Gabriel told us he died once before. So, who knows who is posting now.

On 11/15/2023 1:05 PM, Fritz Feldhase wrote:
> On Wednesday, November 15, 2023 at 9:30:15 PM UTC+1, Chris M. Thomasson wrote:
>> On 11/15/2023 1:08 AM, Adam Polak wrote:
>>> "Task for children" :) Find the difference between the pictures:
>>>
>>> Pict No. 1: 1/2
>>> Pict No. 2: 0.5
>>>
>> 1/2 0.5
>>
>> one half = one half
>>
>> Find the difference:
>>
>> .5 .25 * 2
>>
>> 1/2 (1/4)*2
>
> How about this:
>
> 1/2 * 2 = 1
>
> 0.5 * 2 = 1
>
> Hence 1/2 * 2 = 0.5 * 2.
>
> Dividing both sides by 2 we get:
>
> 1/2 = 0.5
>
> :-P

Indeed! Simple. Now sure what Adam is having trouble understanding it.

Adam sees one half, and 1 / 2 and freaks out. Says they are not the same.

On 11/15/2023 1:45 PM, Chris M. Thomasson wrote:
> On 11/15/2023 1:05 PM, Fritz Feldhase wrote:
>> On Wednesday, November 15, 2023 at 9:30:15 PM UTC+1, Chris M.
>> Thomasson wrote:
>>> On 11/15/2023 1:08 AM, Adam Polak wrote:
>>>> "Task for children" :) Find the difference between the pictures:
>>>>
>>>> Pict No. 1: 1/2
>>>> Pict No. 2: 0.5
>>>>
>>> 1/2 0.5
>>>
>>> one half = one half
>>>
>>> Find the difference:
>>>
>>> .5 .25 * 2
>>>
>>> 1/2 (1/4)*2
>>
>> How about this:
>>
>> 1/2 * 2 = 1
>>
>> 0.5 * 2 = 1
>>
>> Hence 1/2 * 2 = 0.5 * 2.
>>
>> Dividing both sides by 2 we get:
>>
>> 1/2 = 0.5
>>
>> :-P
>
> Indeed! Simple. Now sure what Adam is having trouble understanding it.
>
> Adam sees one half, and 1 / 2 and freaks out. Says they are not the same.

Adam says:

one half

is different than

1/2

wow. I ask him why... The fool says one half is different than me saying
1 divided by two.

Also, Adam has trouble with:

1 equals one

It says, 1, and one, look different on paper to him. Strange Adam...

On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> After serious thinking Adam Polak wrote :
> > środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >> Adam Polak used his keyboard to write :
> >>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>> Adam Polak used his keyboard to write :
> >>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>> I believe it is only by convention that we drop the trailing zeros in
> >>>> the infinite continued decimal expansion representation and call it
> >>>> terminated.
> >>>>
> >>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>> mathematical object.
> >>>
> >>> Yes, conventions, both good ones and those imperfect ones.
> >>>
> >>> "Task for children" :) Find the difference between the pictures:
> >>>
> >>> Pict No. 1 Pict No. 2
> >>>
> >>> 1/2 0.5
> >>>
> >>> I'm sure everyone can spot it.
> >>> Each "picture" above shows a DIFFERENT object - these are two different
> >>> mathematical objects! - the differences are noticeable at first glance.
> >>> Both objects have the same qualitative feature, which is their numerical
> >>> value.
> >> I disagree. Mathematically speaking those are two different symbolic
> >> representations of the same mathematical object.
> >>
> >> [...]
> >
> > You can, of course, disagree with reality, but you can't change it.
> > this: 1
> > this: 23/23
> > this: 1.00
> > this: 1.(0)
> > are completely different objects,
>
> No, they are different symbols for the number one.
>

It's not necessarily that simplistic, for anyone who subscribes to the 'pure set theory as foundations of mathematics' myth.

The first represents the natural number 1, which many say is the set {{}}

The second represents a rational number. Rational numbers are usually 'constructed' as sets of ordered pairs of integers satisfying certain requirements. Integers themselves can be constructed as sets of ordered pairs of natural numbers satisfying some other requirements.

The third and fourth represent a real number. Real numbers are 'constructed' from sets of sets of (sets of?) rational numbers

Anyhow, it ain't necessarily so that they are merely different symbols for the same number one (whatever that is).

On 11/15/2023 1:48 PM, Chris M. Thomasson wrote:
> On 11/15/2023 1:45 PM, Chris M. Thomasson wrote:
>> On 11/15/2023 1:05 PM, Fritz Feldhase wrote:
>>> On Wednesday, November 15, 2023 at 9:30:15 PM UTC+1, Chris M.
>>> Thomasson wrote:
>>>> On 11/15/2023 1:08 AM, Adam Polak wrote:
>>>>> "Task for children" :) Find the difference between the pictures:
>>>>>
>>>>> Pict No. 1: 1/2
>>>>> Pict No. 2: 0.5
>>>>>
>>>> 1/2 0.5
>>>>
>>>> one half = one half
>>>>
>>>> Find the difference:
>>>>
>>>> .5 .25 * 2
>>>>
>>>> 1/2 (1/4)*2
>>>
>>> How about this:
>>>
>>> 1/2 * 2 = 1
>>>
>>> 0.5 * 2 = 1
>>>
>>> Hence 1/2 * 2 = 0.5 * 2.
>>>
>>> Dividing both sides by 2 we get:
>>>
>>> 1/2 = 0.5
>>>
>>> :-P
>>
>> Indeed! Simple. Now sure what Adam is having trouble understanding it.
>>
>> Adam sees one half, and 1 / 2 and freaks out. Says they are not the same.
>
>
> Adam says:
>
> one half
>
> is different than
>
> 1/2
>
> wow. I ask him why... The fool says one half is different than me saying
> 1 divided by two.

For instance, two multiplied by one half equals one.

2 * 1/2 = 1

[...]

one half = 1 half = one half

1 = one = 1
2 = two = 2

On Wednesday, November 15, 2023 at 4:57:05 AM UTC-8, Adam Polak wrote:
>
> mathematics as a science honestly admits that it does not know what the object known as "the number ONE" is
>

And a good thing, too. Philosophers have been arguing for thousands of years about what "the number ONE" is. They are no closer to an answer.

Mathematicians, on the other hand, don't CARE what it is and have been able to use it as a tool and have created the great edifice of modern mathematics (for better of worse).

On Wednesday, November 15, 2023 at 10:51:10 PM UTC+1, FredJeffries wrote:
> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> > After serious thinking Adam Polak wrote :
> > > środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> > >> Adam Polak used his keyboard to write :
> > >>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> > >>>> Adam Polak used his keyboard to write :
> > >>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> > >>>> I believe it is only by convention that we drop the trailing zeros in
> > >>>> the infinite continued decimal expansion representation and call it
> > >>>> terminated.
> > >>>>
> > >>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> > >>>> mathematical object.
> > >>>
> > >>> Yes, conventions, both good ones and those imperfect ones.
> > >>>
> > >>> "Task for children" :) Find the difference between the pictures:
> > >>>
> > >>> Pict No. 1 Pict No. 2
> > >>>
> > >>> 1/2 0.5
> > >>>
> > >>> I'm sure everyone can spot it.
> > >>> Each "picture" above shows a DIFFERENT object - these are two different
> > >>> mathematical objects! - the differences are noticeable at first glance.
> > >>> Both objects have the same qualitative feature, which is their numerical
> > >>> value.
> > >> I disagree. Mathematically speaking those are two different symbolic
> > >> representations of the same mathematical object.
> > >>
> > >> [...]
> > >
> > > You can, of course, disagree with reality, but you can't change it.
> > > this: 1
> > > this: 23/23
> > > this: 1.00
> > > this: 1.(0)
> > > are completely different objects,
> >
> > No, they are different symbols for the number one.
> >
> It's not necessarily that simplistic,
It is (sort of).

Maybe you have seen the following statement in some textbooks

N c Z c Q c R.

There's a reason for that.

Hint: In the context of, say, analysis 23/23 = 1 is clearly a *true* statement..

Won't you think so?

Or do we have to stop the presses?

On Wednesday, November 15, 2023 at 11:09:21 PM UTC+1, Fritz Feldhase wrote:
> On Wednesday, November 15, 2023 at 10:51:10 PM UTC+1, FredJeffries wrote:
> > On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> > > After serious thinking Adam Polak wrote :
> > > > środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> > > >> Adam Polak used his keyboard to write :
> > > >>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> > > >>>> Adam Polak used his keyboard to write :
> > > >>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> > > >>>> I believe it is only by convention that we drop the trailing zeros in
> > > >>>> the infinite continued decimal expansion representation and call it
> > > >>>> terminated.
> > > >>>>
> > > >>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> > > >>>> mathematical object.
> > > >>>
> > > >>> Yes, conventions, both good ones and those imperfect ones.
> > > >>>
> > > >>> "Task for children" :) Find the difference between the pictures:
> > > >>>
> > > >>> Pict No. 1 Pict No. 2
> > > >>>
> > > >>> 1/2 0.5
> > > >>>
> > > >>> I'm sure everyone can spot it.
> > > >>> Each "picture" above shows a DIFFERENT object - these are two different
> > > >>> mathematical objects! - the differences are noticeable at first glance.
> > > >>> Both objects have the same qualitative feature, which is their numerical
> > > >>> value.
> > > >> I disagree. Mathematically speaking those are two different symbolic
> > > >> representations of the same mathematical object.
> > > >>
> > > >> [...]
> > > >
> > > > You can, of course, disagree with reality, but you can't change it.
> > > > this: 1
> > > > this: 23/23
> > > > this: 1.00
> > > > this: 1.(0)
> > > > are completely different objects,
> > >
> > > No, they are different symbols for the number one.
> > >
> > It's not necessarily that simplistic,
> It is (sort of).
>
> Maybe you have seen the following statement in some textbooks
>
> N c Z c Q c R.

See https://en.wikipedia.org/wiki/Number
for example.

> There's a reason for that.
>
> Hint: In the context of, say, analysis 23/23 = 1 is clearly a *true* statement..
>
> Won't you think so?
>
> Or do we have to stop the presses?

Chris M. Thomasson expressed precisely :
> On 11/15/2023 1:05 PM, Fritz Feldhase wrote:
>> On Wednesday, November 15, 2023 at 9:30:15 PM UTC+1, Chris M. Thomasson
>> wrote:
>>> On 11/15/2023 1:08 AM, Adam Polak wrote:
>>>> "Task for children" :) Find the difference between the pictures:
>>>>
>>>> Pict No. 1: 1/2
>>>> Pict No. 2: 0.5
>>>>
>>> 1/2 0.5
>>>
>>> one half = one half
>>>
>>> Find the difference:
>>>
>>> .5 .25 * 2
>>>
>>> 1/2 (1/4)*2
>>
>> How about this:
>>
>> 1/2 * 2 = 1
>>
>> 0.5 * 2 = 1
>>
>> Hence 1/2 * 2 = 0.5 * 2.
>>
>> Dividing both sides by 2 we get:
>>
>> 1/2 = 0.5
>>
>> :-P
>
> Indeed! Simple. Now sure what Adam is having trouble understanding it.
>
> Adam sees one half, and 1 / 2 and freaks out. Says they are not the same.

Timothy Golden IIRC sees this as three symbols, two numerals and an
operation.

on 11/15/2023, FredJeffries supposed :
> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
>> After serious thinking Adam Polak wrote :
>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
>>>> Adam Polak used his keyboard to write :
>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
>>>>>> Adam Polak used his keyboard to write :
>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
>>>>>> I believe it is only by convention that we drop the trailing zeros in
>>>>>> the infinite continued decimal expansion representation and call it
>>>>>> terminated.
>>>>>>
>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
>>>>>> mathematical object.
>>>>>
>>>>> Yes, conventions, both good ones and those imperfect ones.
>>>>>
>>>>> "Task for children" :) Find the difference between the pictures:
>>>>>
>>>>> Pict No. 1 Pict No. 2
>>>>>
>>>>> 1/2 0.5
>>>>>
>>>>> I'm sure everyone can spot it.
>>>>> Each "picture" above shows a DIFFERENT object - these are two different
>>>>> mathematical objects! - the differences are noticeable at first glance.
>>>>> Both objects have the same qualitative feature, which is their numerical
>>>>> value.
>>>> I disagree. Mathematically speaking those are two different symbolic
>>>> representations of the same mathematical object.
>>>>
>>>> [...]
>>>
>>> You can, of course, disagree with reality, but you can't change it.
>>> this: 1
>>> this: 23/23
>>> this: 1.00
>>> this: 1.(0)
>>> are completely different objects,
>>
>> No, they are different symbols for the number one.
>>
>
> It's not necessarily that simplistic, for anyone who subscribes to the 'pure
> set theory as foundations of mathematics' myth.
>
> The first represents the natural number 1, which many say is the set {{}}
>
> The second represents a rational number. Rational numbers are usually
> 'constructed' as sets of ordered pairs of integers satisfying certain
> requirements. Integers themselves can be constructed as sets of ordered pairs
> of natural numbers satisfying some other requirements.
>
> The third and fourth represent a real number. Real numbers are 'constructed'
> from sets of sets of (sets of?) rational numbers
>
> Anyhow, it ain't necessarily so that they are merely different symbols for
> the same number one (whatever that is).

But they are. I would also add that all of those are reals and we have
rationals as embedded in the reals and integers as embedded in the
rationals and naturals as embedded in in the integers.

There is no need for naturals or integers to have fractional parts to
their CDE, to have them implies at least Q.

All of those above symbolize the mathematical concept of the number
one.

On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> on 11/15/2023, FredJeffries supposed :
> > On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> >> After serious thinking Adam Polak wrote :
> >>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >>>> Adam Polak used his keyboard to write :
> >>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>>>> Adam Polak used his keyboard to write :
> >>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>>>> I believe it is only by convention that we drop the trailing zeros in
> >>>>>> the infinite continued decimal expansion representation and call it
> >>>>>> terminated.
> >>>>>>
> >>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>>>> mathematical object.
> >>>>>
> >>>>> Yes, conventions, both good ones and those imperfect ones.
> >>>>>
> >>>>> "Task for children" :) Find the difference between the pictures:
> >>>>>
> >>>>> Pict No. 1 Pict No. 2
> >>>>>
> >>>>> 1/2 0.5
> >>>>>
> >>>>> I'm sure everyone can spot it.
> >>>>> Each "picture" above shows a DIFFERENT object - these are two different
> >>>>> mathematical objects! - the differences are noticeable at first glance.
> >>>>> Both objects have the same qualitative feature, which is their numerical
> >>>>> value.
> >>>> I disagree. Mathematically speaking those are two different symbolic
> >>>> representations of the same mathematical object.
> >>>>
> >>>> [...]
> >>>
> >>> You can, of course, disagree with reality, but you can't change it.
> >>> this: 1
> >>> this: 23/23
> >>> this: 1.00
> >>> this: 1.(0)
> >>> are completely different objects,
> >>
> >> No, they are different symbols for the number one.
> >>
> >
> > It's not necessarily that simplistic, for anyone who subscribes to the 'pure
> > set theory as foundations of mathematics' myth.
> >
> > The first represents the natural number 1, which many say is the set {{}}
> >
> > The second represents a rational number. Rational numbers are usually
> > 'constructed' as sets of ordered pairs of integers satisfying certain
> > requirements. Integers themselves can be constructed as sets of ordered pairs
> > of natural numbers satisfying some other requirements.
> >
> > The third and fourth represent a real number. Real numbers are 'constructed'
> > from sets of sets of (sets of?) rational numbers
> >
> > Anyhow, it ain't necessarily so that they are merely different symbols for
> > the same number one (whatever that is).
> But they are. I would also add that all of those are reals and we have
> rationals as embedded in the reals and integers as embedded in the
> rationals and naturals as embedded in in the integers.
>
> There is no need for naturals or integers to have fractional parts to
> their CDE, to have them implies at least Q.
>
> All of those above symbolize the mathematical concept of the number
> one.
>

https://en.wikipedia.org/wiki/Abuse_of_notation

On Thursday, November 16, 2023 at 12:44:42 AM UTC+1, FredJeffries wrote:
> On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> > on 11/15/2023, FredJeffries supposed :
> > > On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> > >> After serious thinking Adam Polak wrote :
> > >>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> > >>>> Adam Polak used his keyboard to write :
> > >>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> > >>>>>> Adam Polak used his keyboard to write :
> > >>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> > >>>>>> I believe it is only by convention that we drop the trailing zeros in
> > >>>>>> the infinite continued decimal expansion representation and call it
> > >>>>>> terminated.
> > >>>>>>
> > >>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> > >>>>>> mathematical object.
> > >>>>>
> > >>>>> Yes, conventions, both good ones and those imperfect ones.
> > >>>>>
> > >>>>> "Task for children" :) Find the difference between the pictures:
> > >>>>>
> > >>>>> Pict No. 1 Pict No. 2
> > >>>>>
> > >>>>> 1/2 0.5
> > >>>>>
> > >>>>> I'm sure everyone can spot it.
> > >>>>> Each "picture" above shows a DIFFERENT object - these are two different
> > >>>>> mathematical objects! - the differences are noticeable at first glance.
> > >>>>> Both objects have the same qualitative feature, which is their numerical
> > >>>>> value.
> > >>>> I disagree. Mathematically speaking those are two different symbolic
> > >>>> representations of the same mathematical object.
> > >>>>
> > >>>> [...]
> > >>>
> > >>> You can, of course, disagree with reality, but you can't change it.
> > >>> this: 1
> > >>> this: 23/23
> > >>> this: 1.00
> > >>> this: 1.(0)
> > >>> are completely different objects,
> > >>
> > >> No, they are different symbols for the number one.
> > >>
> > >
> > > It's not necessarily that simplistic, for anyone who subscribes to the 'pure
> > > set theory as foundations of mathematics' myth.
> > >
> > > The first represents the natural number 1, which many say is the set {{}}
> > >
> > > The second represents a rational number. Rational numbers are usually
> > > 'constructed' as sets of ordered pairs of integers satisfying certain
> > > requirements. Integers themselves can be constructed as sets of ordered pairs
> > > of natural numbers satisfying some other requirements.
> > >
> > > The third and fourth represent a real number. Real numbers are 'constructed'
> > > from sets of sets of (sets of?) rational numbers
> > >
> > > Anyhow, it ain't necessarily so that they are merely different symbols for
> > > the same number one (whatever that is).
> > But they are. I would also add that all of those are reals and we have
> > rationals as embedded in the reals and integers as embedded in the
> > rationals and naturals as embedded in in the integers.
> >
> > There is no need for naturals or integers to have fractional parts to
> > their CDE, to have them implies at least Q.
> >
> > All of those above symbolize the mathematical concept of the number
> > one.
> >
> https://en.wikipedia.org/wiki/Abuse_of_notation

<facepalm>

środa, 15 listopada 2023 o 15:21:19 UTC+1 FromTheRafters napisał(a):
> After serious thinking Adam Polak wrote :
> > środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >> Adam Polak used his keyboard to write :
> >>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>> Adam Polak used his keyboard to write :
> >>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>> I believe it is only by convention that we drop the trailing zeros in
> >>>> the infinite continued decimal expansion representation and call it
> >>>> terminated.
> >>>>
> >>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>> mathematical object.
> >>>
> >>> Yes, conventions, both good ones and those imperfect ones.
> >>>
> >>> "Task for children" :) Find the difference between the pictures:
> >>>
> >>> Pict No. 1 Pict No. 2
> >>>
> >>> 1/2 0.5
> >>>
> >>> I'm sure everyone can spot it.
> >>> Each "picture" above shows a DIFFERENT object - these are two different
> >>> mathematical objects! - the differences are noticeable at first glance.
> >>> Both objects have the same qualitative feature, which is their numerical
> >>> value.
> >> I disagree. Mathematically speaking those are two different symbolic
> >> representations of the same mathematical object.
> >>
> >> [...]
> >
> > You can, of course, disagree with reality, but you can't change it.
> > this: 1
> > this: 23/23
> > this: 1.00
> > this: 1.(0)
> > are completely different objects,
> No, they are different symbols for the number one.

I see that there is still no argument in your statemet. OK
Gyby: 0.001 and 0.0010000000000000...
were one and the same object: "the number: one thousandth"
it could be always possible to used them interchangeably.
This: 0.001
CANNOT be placed in Cantor's Diagonal Method matrix.
Only this one: 0.0010000000000000...
CAN
This is direct and irrefutable proof that these are two different objects with one common feature: numerical value.

This is where I will end this issue for my part.

Regards, Adam

środa, 15 listopada 2023 o 15:21:19 UTC+1 FromTheRafters napisał(a):
> After serious thinking Adam Polak wrote :
> > środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >> Adam Polak used his keyboard to write :
> >>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>> Adam Polak used his keyboard to write :
> >>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>> I believe it is only by convention that we drop the trailing zeros in
> >>>> the infinite continued decimal expansion representation and call it
> >>>> terminated.
> >>>>
> >>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>> mathematical object.
> >>>
> >>> Yes, conventions, both good ones and those imperfect ones.
> >>>
> >>> "Task for children" :) Find the difference between the pictures:
> >>>
> >>> Pict No. 1 Pict No. 2
> >>>
> >>> 1/2 0.5
> >>>
> >>> I'm sure everyone can spot it.
> >>> Each "picture" above shows a DIFFERENT object - these are two different
> >>> mathematical objects! - the differences are noticeable at first glance.
> >>> Both objects have the same qualitative feature, which is their numerical
> >>> value.
> >> I disagree. Mathematically speaking those are two different symbolic
> >> representations of the same mathematical object.
> >>
> >> [...]
> >
> > You can, of course, disagree with reality, but you can't change it.
> > this: 1
> > this: 23/23
> > this: 1.00
> > this: 1.(0)
> > are completely different objects,
> No, they are different symbols for the number one.

I see that there is still no argument in your statemet. OK

If: 0.001 and 0.0010000000000000...
were one and the same object: "the number: one thousandth"
it could be always possible to used them interchangeably.

This: 0.001
CANNOT be placed in Cantor's Diagonal Method matrix.
Only this one: 0.0010000000000000...
CAN
This is direct and irrefutable proof that these are two different objects with one common feature: numerical value.

This is where I will end this issue for my part.

Regards, Adam

FredJeffries submitted this idea :
> On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
>> on 11/15/2023, FredJeffries supposed :
>>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
>>>> After serious thinking Adam Polak wrote :
>>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
>>>>>> Adam Polak used his keyboard to write :
>>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
>>>>>>>> Adam Polak used his keyboard to write :
>>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
>>>>>>>> I believe it is only by convention that we drop the trailing zeros in
>>>>>>>> the infinite continued decimal expansion representation and call it
>>>>>>>> terminated.
>>>>>>>>
>>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
>>>>>>>> mathematical object.
>>>>>>>
>>>>>>> Yes, conventions, both good ones and those imperfect ones.
>>>>>>>
>>>>>>> "Task for children" :) Find the difference between the pictures:
>>>>>>>
>>>>>>> Pict No. 1 Pict No. 2
>>>>>>>
>>>>>>> 1/2 0.5
>>>>>>>
>>>>>>> I'm sure everyone can spot it.
>>>>>>> Each "picture" above shows a DIFFERENT object - these are two different
>>>>>>> mathematical objects! - the differences are noticeable at first glance.
>>>>>>> Both objects have the same qualitative feature, which is their
>>>>>>> numerical value.
>>>>>> I disagree. Mathematically speaking those are two different symbolic
>>>>>> representations of the same mathematical object.
>>>>>>
>>>>>> [...]
>>>>>
>>>>> You can, of course, disagree with reality, but you can't change it.
>>>>> this: 1
>>>>> this: 23/23
>>>>> this: 1.00
>>>>> this: 1.(0)
>>>>> are completely different objects,
>>>>
>>>> No, they are different symbols for the number one.
>>>>
>>>
>>> It's not necessarily that simplistic, for anyone who subscribes to the
>>> 'pure set theory as foundations of mathematics' myth.
>>>
>>> The first represents the natural number 1, which many say is the set {{}}
>>>
>>> The second represents a rational number. Rational numbers are usually
>>> 'constructed' as sets of ordered pairs of integers satisfying certain
>>> requirements. Integers themselves can be constructed as sets of ordered
>>> pairs of natural numbers satisfying some other requirements.
>>>
>>> The third and fourth represent a real number. Real numbers are
>>> 'constructed' from sets of sets of (sets of?) rational numbers
>>>
>>> Anyhow, it ain't necessarily so that they are merely different symbols for
>>> the same number one (whatever that is).
>> But they are. I would also add that all of those are reals and we have
>> rationals as embedded in the reals and integers as embedded in the
>> rationals and naturals as embedded in in the integers.
>>
>> There is no need for naturals or integers to have fractional parts to
>> their CDE, to have them implies at least Q.
>>
>> All of those above symbolize the mathematical concept of the number
>> one.
>>
>
> https://en.wikipedia.org/wiki/Abuse_of_notation

I'll see that and raise you:

https://en.wikipedia.org/wiki/One_half#Mathematics

czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
> FredJeffries submitted this idea :
> > On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> >> on 11/15/2023, FredJeffries supposed :
> >>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> >>>> After serious thinking Adam Polak wrote :
> >>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >>>>>> Adam Polak used his keyboard to write :
> >>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>>>>>> Adam Polak used his keyboard to write :
> >>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>>>>>> I believe it is only by convention that we drop the trailing zeros in
> >>>>>>>> the infinite continued decimal expansion representation and call it
> >>>>>>>> terminated.
> >>>>>>>>
> >>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>>>>>> mathematical object.
> >>>>>>>
> >>>>>>> Yes, conventions, both good ones and those imperfect ones.
> >>>>>>>
> >>>>>>> "Task for children" :) Find the difference between the pictures:
> >>>>>>>
> >>>>>>> Pict No. 1 Pict No. 2
> >>>>>>>
> >>>>>>> 1/2 0.5
> >>>>>>>
> >>>>>>> I'm sure everyone can spot it.
> >>>>>>> Each "picture" above shows a DIFFERENT object - these are two different
> >>>>>>> mathematical objects! - the differences are noticeable at first glance.
> >>>>>>> Both objects have the same qualitative feature, which is their
> >>>>>>> numerical value.
> >>>>>> I disagree. Mathematically speaking those are two different symbolic
> >>>>>> representations of the same mathematical object.
> >>>>>>
> >>>>>> [...]
> >>>>>
> >>>>> You can, of course, disagree with reality, but you can't change it.
> >>>>> this: 1
> >>>>> this: 23/23
> >>>>> this: 1.00
> >>>>> this: 1.(0)
> >>>>> are completely different objects,
> >>>>
> >>>> No, they are different symbols for the number one.
> >>>>
> >>>
> >>> It's not necessarily that simplistic, for anyone who subscribes to the
> >>> 'pure set theory as foundations of mathematics' myth.
> >>>
> >>> The first represents the natural number 1, which many say is the set {{}}
> >>>
> >>> The second represents a rational number. Rational numbers are usually
> >>> 'constructed' as sets of ordered pairs of integers satisfying certain
> >>> requirements. Integers themselves can be constructed as sets of ordered
> >>> pairs of natural numbers satisfying some other requirements.
> >>>
> >>> The third and fourth represent a real number. Real numbers are
> >>> 'constructed' from sets of sets of (sets of?) rational numbers
> >>>
> >>> Anyhow, it ain't necessarily so that they are merely different symbols for
> >>> the same number one (whatever that is).
> >> But they are. I would also add that all of those are reals and we have
> >> rationals as embedded in the reals and integers as embedded in the
> >> rationals and naturals as embedded in in the integers.
> >>
> >> There is no need for naturals or integers to have fractional parts to
> >> their CDE, to have them implies at least Q.
> >>
> >> All of those above symbolize the mathematical concept of the number
> >> one.
> >>
> >
> > https://en.wikipedia.org/wiki/Abuse_of_notation
> I'll see that and raise you:
>
> https://en.wikipedia.org/wiki/One_half#Mathematics

I've been writing about mathematical objects for 3 days,
and you are sending me Wiki page where the word OBJECT appears ZERO times
and as I see you feel satisfied with yourself :)
Which is amazing considering that the content of the page you indicate confirms and expands on exactly what I've been showing all along.
Namely:
there are different objects, from different systems, that are connected by one quality parameter: a numerical value 0.5

1⁄2th (halfth)
0.12
0.11111111113
0.36
0.48
0.612
0.816
∠
𓐛
חֵצִ
൴
半
༪

czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
> FredJeffries submitted this idea :
> > On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> >> on 11/15/2023, FredJeffries supposed :
> >>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> >>>> After serious thinking Adam Polak wrote :
> >>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >>>>>> Adam Polak used his keyboard to write :
> >>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>>>>>> Adam Polak used his keyboard to write :
> >>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>>>>>> I believe it is only by convention that we drop the trailing zeros in
> >>>>>>>> the infinite continued decimal expansion representation and call it
> >>>>>>>> terminated.
> >>>>>>>>
> >>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>>>>>> mathematical object.
> >>>>>>>
> >>>>>>> Yes, conventions, both good ones and those imperfect ones.
> >>>>>>>
> >>>>>>> "Task for children" :) Find the difference between the pictures:
> >>>>>>>
> >>>>>>> Pict No. 1 Pict No. 2
> >>>>>>>
> >>>>>>> 1/2 0.5
> >>>>>>>
> >>>>>>> I'm sure everyone can spot it.
> >>>>>>> Each "picture" above shows a DIFFERENT object - these are two different
> >>>>>>> mathematical objects! - the differences are noticeable at first glance.
> >>>>>>> Both objects have the same qualitative feature, which is their
> >>>>>>> numerical value.
> >>>>>> I disagree. Mathematically speaking those are two different symbolic
> >>>>>> representations of the same mathematical object.
> >>>>>>
> >>>>>> [...]
> >>>>>
> >>>>> You can, of course, disagree with reality, but you can't change it.
> >>>>> this: 1
> >>>>> this: 23/23
> >>>>> this: 1.00
> >>>>> this: 1.(0)
> >>>>> are completely different objects,
> >>>>
> >>>> No, they are different symbols for the number one.
> >>>>
> >>>
> >>> It's not necessarily that simplistic, for anyone who subscribes to the
> >>> 'pure set theory as foundations of mathematics' myth.
> >>>
> >>> The first represents the natural number 1, which many say is the set {{}}
> >>>
> >>> The second represents a rational number. Rational numbers are usually
> >>> 'constructed' as sets of ordered pairs of integers satisfying certain
> >>> requirements. Integers themselves can be constructed as sets of ordered
> >>> pairs of natural numbers satisfying some other requirements.
> >>>
> >>> The third and fourth represent a real number. Real numbers are
> >>> 'constructed' from sets of sets of (sets of?) rational numbers
> >>>
> >>> Anyhow, it ain't necessarily so that they are merely different symbols for
> >>> the same number one (whatever that is).
> >> But they are. I would also add that all of those are reals and we have
> >> rationals as embedded in the reals and integers as embedded in the
> >> rationals and naturals as embedded in in the integers.
> >>
> >> There is no need for naturals or integers to have fractional parts to
> >> their CDE, to have them implies at least Q.
> >>
> >> All of those above symbolize the mathematical concept of the number
> >> one.
> >>
> >
> > https://en.wikipedia.org/wiki/Abuse_of_notation
> I'll see that and raise you:
>
> https://en.wikipedia.org/wiki/One_half#Mathematics

PS:
What you sent confirms even more clearly that
Cantor's Diagonal matrix DOES NOT INVESTIGATE an object like: "the number: one thousandth" 0.001
but only a completely different OBJECT, specifically this symbol with its specific construction: 0.00100000000000000...

Adam Polak wrote :
> czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
>> FredJeffries submitted this idea :
>>> On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
>>>> on 11/15/2023, FredJeffries supposed :
>>>>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters
>>>>> wrote:
>>>>>> After serious thinking Adam Polak wrote :
>>>>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
>>>>>>>> Adam Polak used his keyboard to write :
>>>>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
>>>>>>>>>> Adam Polak used his keyboard to write :
>>>>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
>>>>>>>>>> I believe it is only by convention that we drop the trailing zeros
>>>>>>>>>> in the infinite continued decimal expansion representation and call
>>>>>>>>>> it terminated.
>>>>>>>>>>
>>>>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
>>>>>>>>>> mathematical object.
>>>>>>>>>
>>>>>>>>> Yes, conventions, both good ones and those imperfect ones.
>>>>>>>>>
>>>>>>>>> "Task for children" :) Find the difference between the pictures:
>>>>>>>>>
>>>>>>>>> Pict No. 1 Pict No. 2
>>>>>>>>>
>>>>>>>>> 1/2 0.5
>>>>>>>>>
>>>>>>>>> I'm sure everyone can spot it.
>>>>>>>>> Each "picture" above shows a DIFFERENT object - these are two
>>>>>>>>> different mathematical objects! - the differences are noticeable at
>>>>>>>>> first glance. Both objects have the same qualitative feature, which
>>>>>>>>> is their numerical value.
>>>>>>>> I disagree. Mathematically speaking those are two different symbolic
>>>>>>>> representations of the same mathematical object.
>>>>>>>>
>>>>>>>> [...]
>>>>>>>
>>>>>>> You can, of course, disagree with reality, but you can't change it.
>>>>>>> this: 1
>>>>>>> this: 23/23
>>>>>>> this: 1.00
>>>>>>> this: 1.(0)
>>>>>>> are completely different objects,
>>>>>>
>>>>>> No, they are different symbols for the number one.
>>>>>>
>>>>>
>>>>> It's not necessarily that simplistic, for anyone who subscribes to the
>>>>> 'pure set theory as foundations of mathematics' myth.
>>>>>
>>>>> The first represents the natural number 1, which many say is the set {{}}
>>>>>
>>>>> The second represents a rational number. Rational numbers are usually
>>>>> 'constructed' as sets of ordered pairs of integers satisfying certain
>>>>> requirements. Integers themselves can be constructed as sets of ordered
>>>>> pairs of natural numbers satisfying some other requirements.
>>>>>
>>>>> The third and fourth represent a real number. Real numbers are
>>>>> 'constructed' from sets of sets of (sets of?) rational numbers
>>>>>
>>>>> Anyhow, it ain't necessarily so that they are merely different symbols
>>>>> for the same number one (whatever that is).
>>>> But they are. I would also add that all of those are reals and we have
>>>> rationals as embedded in the reals and integers as embedded in the
>>>> rationals and naturals as embedded in in the integers.
>>>>
>>>> There is no need for naturals or integers to have fractional parts to
>>>> their CDE, to have them implies at least Q.
>>>>
>>>> All of those above symbolize the mathematical concept of the number
>>>> one.
>>>>
>>>
>>> https://en.wikipedia.org/wiki/Abuse_of_notation
>> I'll see that and raise you:
>>
>> https://en.wikipedia.org/wiki/One_half#Mathematics
>
>
> I've been writing about mathematical objects for 3 days,
> and you are sending me Wiki page where the word OBJECT appears ZERO times
> and as I see you feel satisfied with yourself :)
> Which is amazing considering that the content of the page you indicate
> confirms and expands on exactly what I've been showing all along. Namely:
> there are different objects, from different systems, that are connected by
> one quality parameter: a numerical value 0.5
>
> 1⁄2th (halfth)
> 0.12
> 0.11111111113
> 0.36
> 0.48
> 0.612
> 0.816
> ∠
> ?
> חֵצִ
> ൴
> 半
> ༪

Liar.

Message-ID: <9700dc1b-6ee1-47ad-be75-eec6d8eb25b3n@googlegroups.com>

FromTheRafters was thinking very hard :
> Adam Polak wrote :
>> czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
>>> FredJeffries submitted this idea :
>>>> On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters
>>>> wrote:
>>>>> on 11/15/2023, FredJeffries supposed :
>>>>>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters
>>>>>> wrote:
>>>>>>> After serious thinking Adam Polak wrote :
>>>>>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
>>>>>>>>> Adam Polak used his keyboard to write :
>>>>>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters
>>>>>>>>>> napisał(a):
>>>>>>>>>>> Adam Polak used his keyboard to write :
>>>>>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
>>>>>>>>>>> I believe it is only by convention that we drop the trailing zeros
>>>>>>>>>>> in the infinite continued decimal expansion representation and
>>>>>>>>>>> call it terminated.
>>>>>>>>>>>
>>>>>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
>>>>>>>>>>> mathematical object.
>>>>>>>>>>
>>>>>>>>>> Yes, conventions, both good ones and those imperfect ones.
>>>>>>>>>>
>>>>>>>>>> "Task for children" :) Find the difference between the pictures:
>>>>>>>>>>
>>>>>>>>>> Pict No. 1 Pict No. 2
>>>>>>>>>>
>>>>>>>>>> 1/2 0.5
>>>>>>>>>>
>>>>>>>>>> I'm sure everyone can spot it. Each "picture" above shows a
>>>>>>>>>> DIFFERENT object - these are two different mathematical objects! -
>>>>>>>>>> the differences are noticeable at first glance. Both objects have
>>>>>>>>>> the same qualitative feature, which is their numerical value.
>>>>>>>>> I disagree. Mathematically speaking those are two different symbolic
>>>>>>>>> representations of the same mathematical object.
>>>>>>>>>
>>>>>>>>> [...]
>>>>>>>>
>>>>>>>> You can, of course, disagree with reality, but you can't change it.
>>>>>>>> this: 1 this: 23/23 this: 1.00 this: 1.(0) are completely different
>>>>>>>> objects,
>>>>>>>
>>>>>>> No, they are different symbols for the number one.
>>>>>>>
>>>>>>
>>>>>> It's not necessarily that simplistic, for anyone who subscribes to the
>>>>>> 'pure set theory as foundations of mathematics' myth.
>>>>>>
>>>>>> The first represents the natural number 1, which many say is the set
>>>>>> {{}}
>>>>>>
>>>>>> The second represents a rational number. Rational numbers are usually
>>>>>> 'constructed' as sets of ordered pairs of integers satisfying certain
>>>>>> requirements. Integers themselves can be constructed as sets of ordered
>>>>>> pairs of natural numbers satisfying some other requirements.
>>>>>>
>>>>>> The third and fourth represent a real number. Real numbers are
>>>>>> 'constructed' from sets of sets of (sets of?) rational numbers
>>>>>>
>>>>>> Anyhow, it ain't necessarily so that they are merely different symbols
>>>>>> for the same number one (whatever that is).
>>>>> But they are. I would also add that all of those are reals and we have
>>>>> rationals as embedded in the reals and integers as embedded in the
>>>>> rationals and naturals as embedded in in the integers.
>>>>>
>>>>> There is no need for naturals or integers to have fractional parts to
>>>>> their CDE, to have them implies at least Q.
>>>>>
>>>>> All of those above symbolize the mathematical concept of the number one.
>>>>>
>>>>
>>>> https://en.wikipedia.org/wiki/Abuse_of_notation
>>> I'll see that and raise you:
>>>
>>> https://en.wikipedia.org/wiki/One_half#Mathematics
>>
>>
>> I've been writing about mathematical objects for 3 days, and you are
>> sending me Wiki page where the word OBJECT appears ZERO times
>> and as I see you feel satisfied with yourself :)
>> Which is amazing considering that the content of the page you indicate
>> confirms and expands on exactly what I've been showing all along. Namely:
>> there are different objects, from different systems, that are connected by
>> one quality parameter: a numerical value 0.5
>>
>> 1⁄2th (halfth)
>> 0.12
>> 0.11111111113
>> 0.36
>> 0.48
>> 0.612
>> 0.816
>> ∠
>> ?
>> חֵצִ
>> ൴
>> 半
>> ༪
>
> Liar.
>
> Message-ID: <9700dc1b-6ee1-47ad-be75-eec6d8eb25b3n@googlegroups.com>

Oops, I meant this one (unless I screwed it up again) not that it will
do you any good.

Message-ID: <41af9fca-29c8-4ca3-911a-92b7672281fdn@googlegroups.com>

czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
> FredJeffries submitted this idea :
> > On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> >> on 11/15/2023, FredJeffries supposed :
> >>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> >>>> After serious thinking Adam Polak wrote :
> >>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> >>>>>> Adam Polak used his keyboard to write :
> >>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> >>>>>>>> Adam Polak used his keyboard to write :
> >>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> >>>>>>>> I believe it is only by convention that we drop the trailing zeros in
> >>>>>>>> the infinite continued decimal expansion representation and call it
> >>>>>>>> terminated.
> >>>>>>>>
> >>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> >>>>>>>> mathematical object.
> >>>>>>>
> >>>>>>> Yes, conventions, both good ones and those imperfect ones.
> >>>>>>>
> >>>>>>> "Task for children" :) Find the difference between the pictures:
> >>>>>>>
> >>>>>>> Pict No. 1 Pict No. 2
> >>>>>>>
> >>>>>>> 1/2 0.5
> >>>>>>>
> >>>>>>> I'm sure everyone can spot it.
> >>>>>>> Each "picture" above shows a DIFFERENT object - these are two different
> >>>>>>> mathematical objects! - the differences are noticeable at first glance.
> >>>>>>> Both objects have the same qualitative feature, which is their
> >>>>>>> numerical value.
> >>>>>> I disagree. Mathematically speaking those are two different symbolic
> >>>>>> representations of the same mathematical object.
> >>>>>>
> >>>>>> [...]
> >>>>>
> >>>>> You can, of course, disagree with reality, but you can't change it.
> >>>>> this: 1
> >>>>> this: 23/23
> >>>>> this: 1.00
> >>>>> this: 1.(0)
> >>>>> are completely different objects,
> >>>>
> >>>> No, they are different symbols for the number one.
> >>>>
> >>>
> >>> It's not necessarily that simplistic, for anyone who subscribes to the
> >>> 'pure set theory as foundations of mathematics' myth.
> >>>
> >>> The first represents the natural number 1, which many say is the set {{}}
> >>>
> >>> The second represents a rational number. Rational numbers are usually
> >>> 'constructed' as sets of ordered pairs of integers satisfying certain
> >>> requirements. Integers themselves can be constructed as sets of ordered
> >>> pairs of natural numbers satisfying some other requirements.
> >>>
> >>> The third and fourth represent a real number. Real numbers are
> >>> 'constructed' from sets of sets of (sets of?) rational numbers
> >>>
> >>> Anyhow, it ain't necessarily so that they are merely different symbols for
> >>> the same number one (whatever that is).
> >> But they are. I would also add that all of those are reals and we have
> >> rationals as embedded in the reals and integers as embedded in the
> >> rationals and naturals as embedded in in the integers.
> >>
> >> There is no need for naturals or integers to have fractional parts to
> >> their CDE, to have them implies at least Q.
> >>
> >> All of those above symbolize the mathematical concept of the number
> >> one.
> >>
> >
> > https://en.wikipedia.org/wiki/Abuse_of_notation
> I'll see that and raise you:
>
> https://en.wikipedia.org/wiki/One_half#Mathematics

PS 2:

The first matrixes constructed by Cantor while working on the Diagonal Method looked like this:
1 I MMMMMMMM ...
2 I WWWWWWWW ...
3 I MWMWWMWW ...
4 I MMWMMWMW ...

Can you provide the numerical value represented by any of the objects in the right column?
(rhetorical question)

without having a qualitative parameter such as a numerical value can any of the objects in the right column be "a number" ?
(rhetorical question)

An object/symbol that does not represent any numerical value is neither "a number" nor symbol of "a number".

As part of his research using the Diagonal Method matrix, Cantor did not examine numbers, but completely different objects NOT RELATED to numbers. He studied objects such as: MMWMMWMW ...
more in terms of their "graphic", "geometric" structure than in any way related to a qualitative parameter such as a numerical value.

Using the Diagonal Method matrix, Cantor did not research the numbers! Farther during this works Cantor managed to deceive first himself and then deceive other mathematicians that this is about numbers and quantities in infinite sets of numbers.