FromTheRafters <FTR@nomail.afraid.org> writes:
> WM presented the following explanation :
>> FromTheRafters schrieb am Mittwoch, 25. Oktober 2023 um 17:08:24 UTC+2:
>>> WM presented the following explanation :
>>>> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05
>>>> UTC+2:
>>>>> On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
>>>>>> Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11
>>>>>> UTC+2:
>>>>>>>
>>>>>>> 2. A bijection is not a process.
>>>>> A BIJECTION IS NOT A PROCESS.
>>>>
>>>> A bijection with |N can be executed as a process.
>>
>> According to Cantor. Of course not in reality.
>>
>>> But that doesn't mean it *is* a process.
>>
>> A process is what can be executed as a process.
>
> Explain.

God, you don't expect sense from that pondlife do you?

You of course realise that his argument would make just as much sense
if he replaced the word "process" with "bloozafing".

A bijection can be gimbified as a bloozafing.
That doesn't mean that is is a bloozafing.
A bloozafing is what can be gimbified as a bloozafing.

No - don't explain.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

On 10/29/2023 3:30 PM, Phil Carmody wrote:
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> WM presented the following explanation :
>>> FromTheRafters schrieb am Mittwoch, 25. Oktober 2023 um 17:08:24 UTC+2:
>>>> WM presented the following explanation :
>>>>> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05
>>>>> UTC+2:
>>>>>> On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
>>>>>>> Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11
>>>>>>> UTC+2:
>>>>>>>>
>>>>>>>> 2. A bijection is not a process.
>>>>>> A BIJECTION IS NOT A PROCESS.
>>>>>
>>>>> A bijection with |N can be executed as a process.
>>>
>>> According to Cantor. Of course not in reality.
>>>
>>>> But that doesn't mean it *is* a process.
>>>
>>> A process is what can be executed as a process.
>>
>> Explain.
>
> God, you don't expect sense from that pondlife do you?
>
> You of course realise that his argument would make just as much sense
> if he replaced the word "process" with "bloozafing".
>
> A bijection can be gimbified as a bloozafing.
> That doesn't mean that is is a bloozafing.
> A bloozafing is what can be gimbified as a bloozafing.
>
> No - don't explain.

Never forget:

https://www.thezorklibrary.com/history/port_foozle.html

;^)

On 10/29/2023 3:30 PM, Phil Carmody wrote:
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> WM presented the following explanation :
>>> FromTheRafters schrieb am Mittwoch, 25. Oktober 2023 um 17:08:24 UTC+2:
>>>> WM presented the following explanation :
>>>>> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05
>>>>> UTC+2:
>>>>>> On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
>>>>>>> Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11
>>>>>>> UTC+2:
>>>>>>>>
>>>>>>>> 2. A bijection is not a process.
>>>>>> A BIJECTION IS NOT A PROCESS.
>>>>>
>>>>> A bijection with |N can be executed as a process.
>>>
>>> According to Cantor. Of course not in reality.
>>>
>>>> But that doesn't mean it *is* a process.
>>>
>>> A process is what can be executed as a process.
>>
>> Explain.
>
> God, you don't expect sense from that pondlife do you?
>
> You of course realise that his argument would make just as much sense
> if he replaced the word "process" with "bloozafing".
>
> A bijection can be gimbified as a bloozafing.
> That doesn't mean that is is a bloozafing.
> A bloozafing is what can be gimbified as a bloozafing.
>
> No - don't explain.

God damn Megaboz! ;^)

On Wednesday, October 25, 2023 at 12:45:10 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05 UTC+2:
> > On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
> > > Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11 UTC+2:
> > > >
> > > > A bijection is not a process.
> > > >
> > > [Mückenbla]
> > >
> > A BIJECTION IS NOT A PROCESS.
> >
> A bijection with IN can be executed

What does this even mean, you psychotic asshole full of shit?

1. A BIJECTION IS NOT A PROCESS.

2. A BIJECTION CANNOT BE EXECUTED (whatever that may mean).

Hint: A program can be executed. But a bijection is not a program.

3. A BIJECTION IS NOT A PROGRAM.

Hint: A man can be executed. But a bijection is not a man.

4. A BIJECTION IS NOT A MAN.

5. A BIJECTION IS AN INJECTIVE AND SURJECTIVE FUNCTION.

On Thursday, October 26, 2023 at 8:05:57 PM UTC+2, FromTheRafters wrote:
> WM presented the following explanation :
> >
> > A process is what can be executed as a process.
> >
> Explain.

Pleeze...

See: https://en.wikipedia.org/wiki/Circular_definition

On Monday, October 30, 2023 at 2:28:56 AM UTC+1, Fritz Feldhase wrote:
> On Thursday, October 26, 2023 at 8:05:57 PM UTC+2, FromTheRafters wrote:
> > WM presented the following explanation :
> > >
> > > A process is what can be executed as a process.
> > >
> > Explain.
> >
> Pleeze...

"If someone wants to know what a cellular phone is, telling them that it is a "phone that is cellular" will not be especially illuminating."

> See: https://en.wikipedia.org/wiki/Circular_definition

On Sunday, October 29, 2023 at 5:52:08 PM UTC-3, WM wrote:
> A ordered pair is "indexed" at every element of the matrix B
> Many ordered pairs (m, n) defining positions of the matrix are indexed.
Actually, all ordered pairs. B defines a bijection between |N and |Nx|N

Phil Carmody presented the following explanation :
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> WM presented the following explanation :
>>> FromTheRafters schrieb am Mittwoch, 25. Oktober 2023 um 17:08:24 UTC+2:
>>>> WM presented the following explanation :
>>>>> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05
>>>>> UTC+2:
>>>>>> On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
>>>>>>> Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11
>>>>>>> UTC+2:
>>>>>>>>
>>>>>>>> 2. A bijection is not a process.
>>>>>> A BIJECTION IS NOT A PROCESS.
>>>>>
>>>>> A bijection with |N can be executed as a process.
>>>
>>> According to Cantor. Of course not in reality.
>>>
>>>> But that doesn't mean it *is* a process.
>>>
>>> A process is what can be executed as a process.
>>
>> Explain.
>
> God, you don't expect sense from that pondlife do you?

Of course not.

> You of course realise that his argument would make just as much sense
> if he replaced the word "process" with "bloozafing".

Yes, the most wonderful thing about tiggers is that tiggers are
wonderful things.

https://www.youtube.com/watch?v=VurBc_QpUbs

> A bijection can be gimbified as a bloozafing.
> That doesn't mean that is is a bloozafing.
> A bloozafing is what can be gimbified as a bloozafing.
>
> No - don't explain.

I didn't think that he would, but now he just might.

Phil Carmody presented the following explanation :
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> WM presented the following explanation :
>>> FromTheRafters schrieb am Mittwoch, 25. Oktober 2023 um 17:08:24 UTC+2:
>>>> WM presented the following explanation :
>>>>> Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05
>>>>> UTC+2:
>>>>>> On Tuesday, October 24, 2023 at 1:52:19 PM UTC+2, WM wrote:
>>>>>>> Fritz Feldhase schrieb am Montag, 23. Oktober 2023 um 18:02:11
>>>>>>> UTC+2:
>>>>>>>>
>>>>>>>> 2. A bijection is not a process.
>>>>>> A BIJECTION IS NOT A PROCESS.
>>>>>
>>>>> A bijection with |N can be executed as a process.
>>>
>>> According to Cantor. Of course not in reality.
>>>
>>>> But that doesn't mean it *is* a process.
>>>
>>> A process is what can be executed as a process.
>>
>> Explain.
>
> God, you don't expect sense from that pondlife do you?

Of course not.

> You of course realise that his argument would make just as much sense
> if he replaced the word "process" with "bloozafing".

Yes, the most wonderful thing about tiggers is that tiggers are
wonderful things.

https://www.youtube.com/watch?v=VurBc_QpUbs

> A bijection can be gimbified as a bloozafing.
> That doesn't mean that is is a bloozafing.
> A bloozafing is what can be gimbified as a bloozafing.
>
> No - don't explain.

I didn't think that he would, but now he just might.

Fritz Feldhase schrieb am Sonntag, 29. Oktober 2023 um 20:23:19 UTC+1:
> On Sunday, October 29, 2023 at 10:30:13 AM UTC+1, WM wrote:
>
> > matrix A
> > 1/1, 1/2, 1/3, ...
> > 2/1, 2/2, 2/3, ...
> > 3/1, 3/2, 3/3, ...
> > :
> > is much, much larger than matrix B
> > 1, 2, 4, ...
> > 3, 5, 8, ...
> > 6, 9,13, ...
> > :
> > It is obvious to the naked eye.
> Nope. They have exactly the same "size" (IN x IN),
In the first line of matrix B, 3 and 5 are missing. Therefore you are wrong..

1, 2, 3, 4, 5, 6, 7, ... contains more numbers than
1, 2, 4, 7, ... up to every number.

Belief in magic, happening at the infinite, is not mathematics.

Regards, WM

Fritz Feldhase schrieb am Sonntag, 29. Oktober 2023 um 20:30:31 UTC+1:
> On Sunday, October 29, 2023 at 8:23:19 PM UTC+1, Fritz Feldhase wrote:
> > On Sunday, October 29, 2023 at 10:30:13 AM UTC+1, WM wrote:
> >
> > > matrix A
> > > 1/1, 1/2, 1/3, ...
> > > 2/1, 2/2, 2/3, ...
> > > 3/1, 3/2, 3/3, ...
> > > :
> > > is much, much larger than matrix B
> > > 1, 2, 4, ...
> > > 3, 5, 8, ...
> > > 6, 9,13, ...
> > > :
> > > It is obvious to the naked eye.
> > >
> > Nope. They have exactly the same "size" (namely IN x IN), they are just "filled" with different elements, dumbo.
>
> Hint: The identity criteria for IN x IN matrices is just X = Y iff [X]_i,j = [Y]_i,j for all i,j e IN.
>
> Hence: A = B iff [A]_i,j = [B]_i,j for all i,j e IN.
>
> This would not work if A and B had different "sizes",

It dpes not work. No place occupied by a fraction will ever get indexed.

Regards, WM

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 02:23:16 UTC+1:
> On Wednesday, October 25, 2023 at 12:45:10 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05 UTC+2:

> > > A BIJECTION IS NOT A PROCESS.
> > >
> > A bijection with IN can be executed
>
> What does this even mean,

It means that every pair in the well-order can be found and can be written down.

Regards, WM

William schrieb am Montag, 30. Oktober 2023 um 03:28:33 UTC+1:
> On Sunday, October 29, 2023 at 5:52:08 PM UTC-3, WM wrote:
> > A ordered pair is "indexed" at every element of the matrix B
> > Many ordered pairs (m, n) defining positions of the matrix are indexed.
> Actually, all ordered pairs.

Not those occupied by fractions. That is forced by the definition of the game.

> B defines a bijection between |N and |Nx|N

You cannot understand the game of the OP? What is missing?

Regards, WM

On Monday, October 30, 2023 at 12:32:26 PM UTC+1, WM wrote:
> Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 02:23:16 UTC+1:
> > On Wednesday, October 25, 2023 at 12:45:10 PM UTC+2, WM wrote:
> > > Fritz Feldhase schrieb am Dienstag, 24. Oktober 2023 um 21:26:05 UTC+2:
> > > >
> > > > A BIJECTION IS NOT A PROCESS.
> > > >
> > > A bijection with IN can be executed
> >
> > What does this even mean,
> >
> It means that every pair in the well-order can be found and can be written down.

So A BIJECTION IS NOT A PROCESS. But finding and writing down "pairs in the well-order" [induced by the bijection] may be considered a process.

Wow!

How would you know, Mückenheim?!

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 15:03:17 UTC+1:
> On Monday, October 30, 2023 at 12:22:20 PM UTC+1, WM wrote:
> > Fritz Feldhase schrieb am Sonntag, 29. Oktober 2023 um 20:23:19 UTC+1:
>
> > > Nope. They have exactly the same "size" (IN x IN),
> > >
> > In the first line of matrix B, 3 and 5 are missing. Therefore you are wrong.
> I was talking about "the size" of the matrices

Their size is measured by their contents.

> Hint (1): The two matrices (a_i,j)_(i e {1}, j e IN) = [1, 2, 3, ...] and (b_i,j)_(i e {1}, j e IN) = [2, 4, 6, ...] have the same "size",

No, that is only the belief of matheologians, contradicted by the OP.

Regards, WM

On Monday, October 30, 2023 at 8:35:17 AM UTC-3, WM wrote:
> William schrieb am Montag, 30. Oktober 2023 um 03:28:33 UTC+1:
> > On Sunday, October 29, 2023 at 5:52:08 PM UTC-3, WM wrote:
> > > A ordered pair is "indexed" at every element of the matrix B
> > > Many ordered pairs (m, n) defining positions of the matrix are indexed.
> > Actually, all ordered pairs.
> Not those occupied by fractions

??? All positions in B are occupied by natural numbers B, which you have noted exists,
defines a bijection between |N and |Nx|N.

On 10/30/2023 12:34 PM, WM wrote:
> Fritz Feldhase schrieb am Montag,
> 30. Oktober 2023 um 15:03:17 UTC+1:
>> On Monday, October 30, 2023
>> at 12:22:20 PM UTC+1, WM wrote:
>>> Fritz Feldhase schrieb am Sonntag,
>>> 29. Oktober 2023 um 20:23:19 UTC+1:

>>>> Nope.
>>>> They have exactly the same "size"
>>>> (IN x IN),
>>>
>>> In the first line of matrix B,
>>> 3 and 5 are missing.
>>> Therefore you are wrong.

Some sets are a set with a different "size"
when two elements are removed.

Some sets are a set with the same "size"
when two elements are removed.

The set ⟨0,..,n⟩ which is
minimally-each-visible-up-to-n
is the first kind of set.

The set ℕ which is
minimally-each-visible
is the second kind of set.

>> I was talking about "the size" of
>> the matrices
>
> Their size is measured by their contents.

If, for each element in A,
there is a unique element in B,
then B is at least as "large" as A

If _both_
for each element in A,
there is a unique element in B
_and_
for each element in B,
there is a unique element in A,
then
B is the same "size" as A
(Cantor-Schröder-Bernstein)

>> Hint (1):
>> The two matrices
>> (a_i,j)_(i e {1}, j e IN) = [1, 2, 3, ...] and
>> (b_i,j)_(i e {1}, j e IN) = [2, 4, 6, ...]
>> have the same "size",
>
> No,

Yes.
_Both_
for each element in [1, 2, 3, ...]
there is a unique element in [2, 4, 6, ...]
_and_
for each element in [2, 4, 6, ...]
there is a unique element in [1, 2, 3, ...]

[1, 2, 3, ...] and [2, 4, 6, ...]
have the same "size".

> that is only the belief of matheologians,
> contradicted by the OP.

| "Just the place for a Snark!" the Bellman cried,
| As he landed his crew with care;
| Supporting each man on the top of the tide
| By a finger entwined in his hair.
| | "Just the place for a Snark! I have said it twice:
| That alone should encourage the crew.
| Just the place for a Snark! I have said it thrice:
| What I tell you three times is true."
| -- Lewis Carroll, "The Hunting of the Snark" (1874-6)

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 15:27:13 UTC+1:

> Hint: B = (b_n,m)_(n,m e IN) is defined with b_n,m = m + (m + n - 1)(m + n - 2)/2 for all n,m e IN.

Not for those ositions (n, m) inhabited by fractions p/q. Observe and obey the rules of the game.
>
> > You cannot understand [this]?
>
> Yeah, you cannot understand this? What is missing?

All matrix positions inhabited by fractions remain without indeX by the rules.

Regards, WM

William schrieb am Montag, 30. Oktober 2023 um 18:10:00 UTC+1:
> On Monday, October 30, 2023 at 8:35:17 AM UTC-3, WM wrote:
> > William schrieb am Montag, 30. Oktober 2023 um 03:28:33 UTC+1:
> > > On Sunday, October 29, 2023 at 5:52:08 PM UTC-3, WM wrote:
> > > > A ordered pair is "indexed" at every element of the matrix B
> > > > Many ordered pairs (m, n) defining positions of the matrix are indexed.
> > > Actually, all ordered pairs.
> > Not those occupied by fractions
> ??? All positions in B are occupied by natural numbers B, which you have noted exists,

Of course, but B is smaller than A because, according to the rules, never a fraction is sitting at an indexed position. But all the fractions remain within the matrix.

Can't you understand the rules publsihed in the OP? Or don't you accept them? Why?

Regards, WM

Jim Burns schrieb am Montag, 30. Oktober 2023 um 19:25:38 UTC+1:
> On 10/30/2023 12:34 PM, WM wrote:
> > Fritz Feldhase schrieb am Montag,
> > 30. Oktober 2023 um 15:03:17 UTC+1:
> >> On Monday, October 30, 2023
> >> at 12:22:20 PM UTC+1, WM wrote:
> >>> Fritz Feldhase schrieb am Sonntag,
> >>> 29. Oktober 2023 um 20:23:19 UTC+1:

> >>> In the first line of matrix B,
> >>> 3 and 5 are missing.
> >>> Therefore you are wrong.
> Some sets are a set with a different "size"
> when two elements are removed.
>
> Some sets are a set with the same "size"
> when two elements are removed.

No, this silly idea is refuted in the OP.

> B is the same "size" as A

B is smaller than A because, according to the rules, never a fraction is sitting at an indexed position. But all the fractions remain within the matrix.

Can't you understand the rules published in the OP? Or don't you accept them? Why?

Regards, WM

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 20:30:20 UTC+1:
> On Monday, October 30, 2023 at 7:48:17 PM UTC+1, WM wrote:
>
> > but B is smaller than A
>
> No, B is NOT "smaller than" A. Both are IN x IN matrices (i.e. have the same "size").
>
> But the set of elements of B is a proper subset of the set of elements of A. I guess that's what you MEAN.

What I mean is that A contains B as a submatrix but A contains also fractions which sit at places not belonging to B because they are not indexed, contrary to all places of B.

Regards, WM

On Monday, October 30, 2023 at 7:51:07 PM UTC+1, WM wrote:
> Jim Burns schrieb am Montag, 30. Oktober 2023 um 19:25:38 UTC+1:
> >
> > Some sets are [of] a different "size"
> > when two elements are removed. (a)
> >
> > Some sets are [of] the same "size"
> > when two elements are removed. (b)

Right.

(a) {1, 2, 3} vs. {3}

(b) {1, 2, 3, 4, ...} vs {3, 4, 5, ...} or [0, 1] vs. (0, 1).

> > B is the same "size" as A
> >
> B is smaller than A because <bla>

No, B is NOT "smaller than" A. Both are IN x IN matrices (i.e. have the same "size").

But the set of elements of B is a proper subset of the set of elements of A.. I guess that's what you MEAN.

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 20:37:10 UTC+1:
> On Monday, October 30, 2023 at 8:33:59 PM UTC+1, WM wrote:
> > Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 20:30:20 UTC+1:
> > >
> > > B is NOT "smaller than" A. Both are IN x IN matrices (i.e. have the same "size").
> > >
> > > But the set of elements of B is a proper subset of the set of elements of A. I guess that's what you MEAN.
> > >
> > What I mean is that A contains B as a submatrix
> Please define /submatrix/, then show/prove your claim. Than you.

The submatrix covers the upper left part of the matrix.
>
> Hint: Both - A and B - are IN x IN matrices (i.e. have the same "size" or "format", etc.).

For the visible part that is true. Both, A and B, contain as indices i and j the potentially infinite collection ℕ_def. But A contains more dark indices because A contains positions (m, n) inhabited by fractions which cannot be determined as individuals.

Regards, WM

Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 20:43:41 UTC+1:
> On Monday, October 30, 2023 at 8:33:59 PM UTC+1, WM wrote:
> > A contains [elements] which sit at places not belonging to B because
>
> Nope. The places where elements "reside" are the same in both matrices A and B. They are "specified" by i,j e IN, you know.

B contains only natural numbers. A contains natural numbers and all positive fractions.
>
> Now the i,j usd for the matrix A are from IN, and the i,j used for the matrix B are from IN too. Both matrices, A and B, have the same "index set".
>
> Maybe you ment: "A contains elements not belonging to B."

And not sitting at indexed positions (m, n).

Regards, WM

On 10/30/2023 12:33 PM, WM wrote:
> Fritz Feldhase schrieb am Montag, 30. Oktober 2023 um 20:30:20 UTC+1:
>> On Monday, October 30, 2023 at 7:48:17 PM UTC+1, WM wrote:
>>
>>> but B is smaller than A
>>
>> No, B is NOT "smaller than" A. Both are IN x IN matrices (i.e. have the same "size").
>>
>> But the set of elements of B is a proper subset of the set of elements of A. I guess that's what you MEAN.
>
> What I mean is that A contains B as a submatrix but A contains also fractions which sit at places not belonging to B because they are not indexed, contrary to all places of B.

Cantor pairing indexes them.