I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:

**start Bing's answer**

The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.

Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.

Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.

**end Bing's answer**

Le 16/04/2023 à 20:22, David Petry a écrit :
>
> I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
>
> **start Bing's answer**
>
> The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
>
> Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
>
> Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
>
> **end Bing's answer**

You have a utterly narrow point of view David:

https://dash.harvard.edu/bitstream/handle/1/3715468/suber_infinite.html

I've always wondered why are ultra-finitists of your kind, including
(unfortunately) Professor Wolfgang Mückenheim so psychologically
reluctant to accept one of most impressive conquest of the Human
mind... Not only all of you are horrible when it comes to logical
and honest thinking but you seem to have developed some kind of
mental phobic. What bother you so much in having Humanity being
able to build a rigorous logical frame handling infinities.

Is that some kind of religious taboo? Brain damage?

Python presented the following explanation :
> Le 16/04/2023 à 20:22, David Petry a écrit :
>>
>> I'm just playing around here. I asked Bing AI if the actual infinite is
>> part of mathematics, and it gave me this answer:
>>
>> **start Bing's answer**
>>
>> The question of whether the actual infinite is part of mathematics is a
>> philosophical one that has been debated for centuries. The actual infinite
>> involves the acceptance of infinite entities as given, actual and completed
>> objects, such as the set of natural numbers or an infinite sequence of
>> rational numbers. The actual infinite is contrasted with the potential
>> infinite, which involves a non-terminating process that produces a sequence
>> with no last element, such as adding 1 to the previous number. The
>> potential infinite is often formalized using the concept of limit.
>>
>> Some philosophers and mathematicians have argued that the actual infinite
>> is impossible or paradoxical, because it goes against the laws of nature
>> and our everyday experience . They have also raised various logical
>> problems and contradictions that arise from assuming the existence of
>> actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's
>> paradox. Others have defended the actual infinite as a legitimate and
>> useful concept in mathematics and logic, and have developed rigorous
>> theories and methods to deal with it, such as set theory, transfinite
>> arithmetic, and non-standard analysis. They have also argued that the
>> actual infinite is consistent and coherent, and that it does not entail any
>> absurdities or contradictions if properly understood and applied.
>>
>> Therefore, the answer to whether the actual infinite is part of mathematics
>> depends on one's philosophical views and assumptions about the nature of
>> infinity, reality, and mathematics. There is no definitive or universally
>> accepted answer to this question, but rather different perspectives and
>> arguments that can be evaluated and compared.
>>
>> **end Bing's answer**
>
> You have a utterly narrow point of view David:

Which he did not exhibit by quoting someone else's point of view --
even if it *is* a bot's point of view.

The continuum hypothesis starts at a fundamental size of infinity...
There are larger and smaller sizes projected beyond it...

Mitchell Raemsch

On Sunday, April 16, 2023 at 11:22:36 AM UTC-7, David Petry wrote:
> I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
>
> **start Bing's answer**
>
> The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
>
> Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
>
> Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
>
> **end Bing's answer**

How many independent definitions of continuity are there?

On Sunday, April 16, 2023 at 4:45:30 PM UTC-7, Ross Finlayson wrote:
> On Sunday, April 16, 2023 at 11:22:36 AM UTC-7, David Petry wrote:
> > I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
> >
> > **start Bing's answer**
> >
> > The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
> >
> > Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
> >
> > Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
> >
> > **end Bing's answer**
> How many independent definitions of continuity are there?

There is moving continuity at zero and the infinitely small.
They happen together.

On Sunday, April 16, 2023 at 8:22:36 PM UTC+2, David Petry wrote:
> I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
>
> **start Bing's answer**
>
> The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
>
> Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
>
> Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
>
> **end Bing's answer**

Ultimately it seems simply a question of whether the fundamental fabric of the universe
is discrete or continuous.
Energy and matter seem discrete in the sense that there seem to be fundamental
limits on quantities. The Planck scale of time and space and constraints on observable
aspects like time and energy or (radial or angular) momentum and position.

Does this also hold for information?
Are there fields of information similar to fields associated with fermions and bosons?

On Sunday, April 16, 2023 at 5:14:14 PM UTC-7, sobriquet wrote:
> On Sunday, April 16, 2023 at 8:22:36 PM UTC+2, David Petry wrote:
> > I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
> >
> > **start Bing's answer**
> >
> > The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
> >
> > Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
> >
> > Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
> >
> > **end Bing's answer**
> Ultimately it seems simply a question of whether the fundamental fabric of the universe
> is discrete or continuous.
> Energy and matter seem discrete in the sense that there seem to be fundamental
> limits on quantities. The Planck scale of time and space and constraints on observable
> aspects like time and energy or (radial or angular) momentum and position..
>
> Does this also hold for information?
> Are there fields of information similar to fields associated with fermions and bosons?

Light waves are discrete quantities of energy. Dimension is continuous.
Both sides are represented in science. You can't leave either
of these physicals out. Gravity is a continuous field... so is its time.

On Monday, April 17, 2023 at 5:57:06 AM UTC+10, Python wrote:
> Le 16/04/2023 à 20:22, David Petry a écrit :
> >
> > I'm just playing around here. I asked Bing AI if the actual infinite is part of mathematics, and it gave me this answer:
> >
> > **start Bing's answer**
> >
> > The question of whether the actual infinite is part of mathematics is a philosophical one that has been debated for centuries. The actual infinite involves the acceptance of infinite entities as given, actual and completed objects, such as the set of natural numbers or an infinite sequence of rational numbers. The actual infinite is contrasted with the potential infinite, which involves a non-terminating process that produces a sequence with no last element, such as adding 1 to the previous number. The potential infinite is often formalized using the concept of limit.
> >
> > Some philosophers and mathematicians have argued that the actual infinite is impossible or paradoxical, because it goes against the laws of nature and our everyday experience . They have also raised various logical problems and contradictions that arise from assuming the existence of actual infinities, such as Zeno's paradoxes, Hilbert's hotel, or Cantor's paradox. Others have defended the actual infinite as a legitimate and useful concept in mathematics and logic, and have developed rigorous theories and methods to deal with it, such as set theory, transfinite arithmetic, and non-standard analysis. They have also argued that the actual infinite is consistent and coherent, and that it does not entail any absurdities or contradictions if properly understood and applied.
> >
> > Therefore, the answer to whether the actual infinite is part of mathematics depends on one's philosophical views and assumptions about the nature of infinity, reality, and mathematics. There is no definitive or universally accepted answer to this question, but rather different perspectives and arguments that can be evaluated and compared.
> >
> > **end Bing's answer**
> You have a utterly narrow point of view David:
>
> https://dash.harvard.edu/bitstream/handle/1/3715468/suber_infinite.html
>
> I've always wondered why are ultra-finitists of your kind, including
> (unfortunately) Professor Wolfgang Mückenheim so psychologically
> reluctant to accept one of most impressive conquest of the Human
> mind... Not only all of you are horrible when it comes to logical
> and honest thinking but you seem to have developed some kind of
> mental phobic. What bother you so much in having Humanity being
> able to build a rigorous logical frame handling infinities.
>
> Is that some kind of religious taboo? Brain damage?

0 (ZERO) ENGINEERING UTILITY
0 (ZERO) MATHEMATICS UTILITY

The whole fabric of hyper-infinities is based on *PRUVING* finite mathematics is WRONG!

when finite mathematics is complete!

KINDERGARDEN DERO MATHS

[1]23
4[5]6
78[9]

260 is MISSING! that is all HYPER-MATHETICS is based on

and it DOESNT EVEN WORK FOR INFINITE LISTS!

www.new-math.com

Clasically Real Numbers have 2 types:
RATIONAL
IRRATIONAL

Rational Numbers have a repeating pattern of digits.

0.333...
0.1212...

Consider Champernownes Constant
0.1234567891011121314..

It has a repeating general pattern but not a repeating pattern of digits.

A more general CLASS of REAL NUMBERS is:

REPEATING GENERAL PATTERN
NO REPEATING GENERAL PATTERN

This is
Computable Numbers (FINITE INFORMATION ENTROPY - FILESIZE)
Random Numbers (INFINITE INFORMATION ENTROPY - FILESIZE)

COUNTABLE(R)
REAL_1_digit = TM1(digit)
REAL_2_digit = random(0,1)
REAL_3_digit = TM2(digit)
REAL_4_digit = random(0,1)
and so on

This list contains all computable reals
and all random numbers.

The SET OF FINITE PREFIXES

0.3
0.33
0.333
0.3333
....

contains all sequences of 3
except the infinite sequence of 3s

This is because there is a DISCONTINUITY
AS width-->oo #3s-->oo

BUT when WIDTH=oo #3s is FINITE!

======================
NOW CONSIDER FINITE PREFIXES of COUNTABLE(R)

0.0
0.1

0.00
0.01
0.10
0.11

AND SO ON

AS width-->oo size(all finite prefixes)-->oo

ALSO

AS width=oo size(all finite prefixes) = oo

THERE IS NO DICONTINUITY

so

WIDTH( all possible sequences ) = oo

ALL REALS ARE LISTABLE!

=====================

LETS APPLY CANTORS ANTI-DIAGONAL PROOF

-----------------------------------------

SAY
REALS
0.111..
0.000..
0.100..
...

DIAG
0.[1]11..
0.0[0]0..
0.10[0]..
...

DIAG = 0.100...

PERMUTE DIAGONAL
0.1[1]1..
0.[0]00..
0.10[0]..
...

DIAG = 0.010..

So the list can be sorted to give different DIAGONALS

================================
GIVEN A RANDOM NUMBER R

SAY
R = 0.010..

Then the LIST CAN BE SORTED to fit R onto the DIAGONAL
with PROB=1

So you can CALCULATE A DIAGONAL (RANDOMLY)
WITHOUT INSPECTING THE LIST

CANTORS PROOF METHOD PROVES
A RANDOM ANTI-DIAGONAL IS MISSING FROM THE LIST
WITH PROB=1

CANTOR:
WITH PROB=1 A RANDOM NUMBER IS MISSING FROM THE LIST

-----------------------------------------

REALS_2_digit = random(0,1)
REALS_4_digit = random(0,1)
...

Every EVEN real is a random number

======================
Given countably infinite random numbers on the list of REALS
PROB( R on LIST ) > 0

CANTOR PROVES
PROB( R on LIST ) = 0

CONTRADICTION
CANTOR IS DISPROVEN

|R|=|N|