Le jeudi 25 mai 2023 à 23:36:28 UTC+2, Chris M. Thomasson a écrit :
> On 5/25/2023 7:24 AM, PengKuan Em wrote:
> I can create a symbol, call it xxx[0].
>
> I can say xxx[0] represents all of the infinity between 0 and 1.
>
> I can say xxx[1] represents all of the infinity between 1 and 2.
>
> Well, xxx[n] is infinity in and of itself. It is never full.

Sorry, I may have misunderstood your "infinity is never full".

When I say that infinity is full I mean: the set in 1 to 1 with the set N makes N full, that is, each i belonging to N has an correspondent, and seen as a box, i is full and N is full in consequence.

I think we are talking 2 different things.

KP

On 5/26/2023 2:19 PM, PengKuan Em wrote:
> Le jeudi 25 mai 2023 à 23:36:28 UTC+2, Chris M. Thomasson a écrit :
>> On 5/25/2023 7:24 AM, PengKuan Em wrote:
>> I can create a symbol, call it xxx[0].
>>
>> I can say xxx[0] represents all of the infinity between 0 and 1.
>>
>> I can say xxx[1] represents all of the infinity between 1 and 2.
>>
>> Well, xxx[n] is infinity in and of itself. It is never full.
>
> Sorry, I may have misunderstood your "infinity is never full".
>
> When I say that infinity is full I mean: the set in 1 to 1 with the set N makes N full, that is, each i belonging to N has an correspondent, and seen as a box, i is full and N is full in consequence.
>
> I think we are talking 2 different things.

I think so, sorry about that. ;^o

My analogy of an infinite waterfall pouring into a sack that can hold an
infinite amount of water, well, the sack is never 100% full in a sense
because it can always hold more, and more water... Forevermore.

Saying the sack is full to me implies that it cannot hold any more water...

Le vendredi 26 mai 2023 à 23:34:58 UTC+2, Chris M. Thomasson a écrit :
> On 5/26/2023 2:19 PM, PengKuan Em wrote:
> > Le jeudi 25 mai 2023 à 23:36:28 UTC+2, Chris M. Thomasson a écrit :
> >> On 5/25/2023 7:24 AM, PengKuan Em wrote:
> >> I can create a symbol, call it xxx[0].
> >>
> >> I can say xxx[0] represents all of the infinity between 0 and 1.
> >>
> >> I can say xxx[1] represents all of the infinity between 1 and 2.
> >>
> >> Well, xxx[n] is infinity in and of itself. It is never full.
> >
> > Sorry, I may have misunderstood your "infinity is never full".
> >
> > When I say that infinity is full I mean: the set in 1 to 1 with the set N makes N full, that is, each i belonging to N has an correspondent, and seen as a box, i is full and N is full in consequence.
> >
> > I think we are talking 2 different things.
> I think so, sorry about that. ;^o
>
> My analogy of an infinite waterfall pouring into a sack that can hold an
> infinite amount of water, well, the sack is never 100% full in a sense
> because it can always hold more, and more water... Forevermore.
>
> Saying the sack is full to me implies that it cannot hold any more water....

I see. In fact, what you say is to fill an infinite space ( number line) with finite quantity (finite number). In this case, the infinite space is never full.

KP

Python <python@invalid.org> writes:
> Ben Bacarisse wrote:
>> FredJeffries <fredjeffries@gmail.com> writes:
>>
>>> You have stumbled onto the difference between a 'potentially infinite'
>>> process and an 'actually infinite' set. Contrary to popular opinion
>>> around here, there is room for both tools.
>>
>> Who here does not accept the validity of potentially infinite processes?
>>
>> There is one poster who talks about "potentially infinite sets" but they
>> have crazy theorems (well, conjectures actually since no proofs have
>> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
>>
>> Do you think there is also room for potentially infinite /sets/ here?
>> If so, can you give an example of a theorem about them (with proof) that
>> shows how they are different to the usual infinite sets?
>
> Given the increasing dementia in Wolfgang Mückenheim's mind this days
> ("first unit fraction", sigh...) my guess is that the next breakthrough
> in Mückenmath (aka "patamathematics") will be to distinguish actual
> finite sets and potential finite sets :-))

I'm looking forward to a heated argument over the difference between
actual empty sets and potentially empty sets.

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/

FromTheRafters <FTR@nomail.afraid.org> writes:
> Ben Bacarisse pretended :
>> FredJeffries <fredjeffries@gmail.com> writes:
>>
>>> You have stumbled onto the difference between a 'potentially infinite'
>>> process and an 'actually infinite' set. Contrary to popular opinion
>>> around here, there is room for both tools.
>>
>> Who here does not accept the validity of potentially infinite processes?
>>
>> There is one poster who talks about "potentially infinite sets" but they
>> have crazy theorems (well, conjectures actually since no proofs have
>> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
>>
>> Do you think there is also room for potentially infinite /sets/ here?
>> If so, can you give an example of a theorem about them (with proof) that
>> shows how they are different to the usual infinite sets?
>
> I have mentioned previously something very close.
>
> Studying the mathematical (set theoretical) structure of computer
> viruses with the instruction set, the set of states, the set of
> symbols, the number of heads, number of tapes, on a suitable stored
> program random access machine with attached background storage. All
> sets are finite except for the tape. I was introduced to the concept
> of a 'semi-infinite' tape which was explained to be "as big as it
> needs to be" and not to worry too much about it.

We were taught "unbounded" rather than infinite.
Semi-infinite I don't approve of, as it implies it has one bound.

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 Thursday, May 25, 2023 at 4:44:37 PM UTC+2, FromTheRafters wrote:

> [...] All sets are finite except for the tape. I was introduced to the concept of
> a 'semi-infinite' tape which was explained to be "as big as it needs to
> be" and not to worry too much about it.

Right. Other authors use the term "potentially infinite" in this context.

So "the tape" can grow (if need be).

On Thursday, June 1, 2023 at 12:22:44 PM UTC-7, Phil Carmody wrote:
> FromTheRafters <F...@nomail.afraid.org> writes:
> > Ben Bacarisse pretended :
> >> FredJeffries <fredje...@gmail.com> writes:
> >>
> >>> You have stumbled onto the difference between a 'potentially infinite'
> >>> process and an 'actually infinite' set. Contrary to popular opinion
> >>> around here, there is room for both tools.
> >>
> >> Who here does not accept the validity of potentially infinite processes?
> >>
> >> There is one poster who talks about "potentially infinite sets" but they
> >> have crazy theorems (well, conjectures actually since no proofs have
> >> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
> >>
> >> Do you think there is also room for potentially infinite /sets/ here?
> >> If so, can you give an example of a theorem about them (with proof) that
> >> shows how they are different to the usual infinite sets?
> >
> > I have mentioned previously something very close.
> >
> > Studying the mathematical (set theoretical) structure of computer
> > viruses with the instruction set, the set of states, the set of
> > symbols, the number of heads, number of tapes, on a suitable stored
> > program random access machine with attached background storage. All
> > sets are finite except for the tape. I was introduced to the concept
> > of a 'semi-infinite' tape which was explained to be "as big as it
> > needs to be" and not to worry too much about it.
>
> We were taught "unbounded" rather than infinite.
> Semi-infinite I don't approve of, as it implies it has one bound.
> 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/

Like, "the upper half-plane"?

I think it usually means "half the infinite" (i.e. in terms of symmetry and the unbounded).

On Thursday, June 1, 2023 at 12:21:01 PM UTC-7, Phil Carmody wrote:
> Python <pyt...@invalid.org> writes:
> > Ben Bacarisse wrote:
> >> FredJeffries <fredje...@gmail.com> writes:
> >>
> >>> You have stumbled onto the difference between a 'potentially infinite'
> >>> process and an 'actually infinite' set. Contrary to popular opinion
> >>> around here, there is room for both tools.
> >>
> >> Who here does not accept the validity of potentially infinite processes?
> >>
> >> There is one poster who talks about "potentially infinite sets" but they
> >> have crazy theorems (well, conjectures actually since no proofs have
> >> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
> >>
> >> Do you think there is also room for potentially infinite /sets/ here?
> >> If so, can you give an example of a theorem about them (with proof) that
> >> shows how they are different to the usual infinite sets?
> >
> > Given the increasing dementia in Wolfgang Mückenheim's mind this days
> > ("first unit fraction", sigh...) my guess is that the next breakthrough
> > in Mückenmath (aka "patamathematics") will be to distinguish actual
> > finite sets and potential finite sets :-))
>
> I'm looking forward to a heated argument over the difference between
> actual empty sets and potentially empty sets.
>
> 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/

Imagine a set-like object that doesn't have access to its members,
only given members by their value, then various accessors that
can enumerate disjoint domains, it can model "empty" with
respect to one while "non-empty" with respect to another.

You might wonder more whether "there's a unique empty set"
or empty sets are typed" or "the empty set kind of contains
infinitely many copies of the empty set " (which is kind of a thing
in the non-well-founded set theory, that structurally it's like so
and all its accesses are as per so).

Then there's to be considered various topologies,
and the differences of something like
"nested intervals: always non-empty", and
"vanishing interval: always empty".

This isn't an argument per se, but, those are things.

On 6/1/2023 6:15 PM, Ross Finlayson wrote:
> On Thursday, June 1, 2023 at 12:22:44 PM UTC-7, Phil Carmody wrote:
>> FromTheRafters <F...@nomail.afraid.org> writes:
>>> Ben Bacarisse pretended :
>>>> FredJeffries <fredje...@gmail.com> writes:
>>>>
>>>>> You have stumbled onto the difference between a 'potentially infinite'
>>>>> process and an 'actually infinite' set. Contrary to popular opinion
>>>>> around here, there is room for both tools.
>>>>
>>>> Who here does not accept the validity of potentially infinite processes?
>>>>
>>>> There is one poster who talks about "potentially infinite sets" but they
>>>> have crazy theorems (well, conjectures actually since no proofs have
>>>> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
>>>>
>>>> Do you think there is also room for potentially infinite /sets/ here?
>>>> If so, can you give an example of a theorem about them (with proof) that
>>>> shows how they are different to the usual infinite sets?
>>>
>>> I have mentioned previously something very close.
>>>
>>> Studying the mathematical (set theoretical) structure of computer
>>> viruses with the instruction set, the set of states, the set of
>>> symbols, the number of heads, number of tapes, on a suitable stored
>>> program random access machine with attached background storage. All
>>> sets are finite except for the tape. I was introduced to the concept
>>> of a 'semi-infinite' tape which was explained to be "as big as it
>>> needs to be" and not to worry too much about it.
>>
>> We were taught "unbounded" rather than infinite.
>> Semi-infinite I don't approve of, as it implies it has one bound.
>> 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/
>
> Like, "the upper half-plane"?

Reminds of a half plane to disc conformal mapping.

>
> I think it usually means "half the infinite" (i.e. in terms of symmetry and the unbounded).
>

On Thursday, June 1, 2023 at 6:30:52 PM UTC-7, Chris M. Thomasson wrote:
> On 6/1/2023 6:15 PM, Ross Finlayson wrote:
> > On Thursday, June 1, 2023 at 12:22:44 PM UTC-7, Phil Carmody wrote:
> >> FromTheRafters <F...@nomail.afraid.org> writes:
> >>> Ben Bacarisse pretended :
> >>>> FredJeffries <fredje...@gmail.com> writes:
> >>>>
> >>>>> You have stumbled onto the difference between a 'potentially infinite'
> >>>>> process and an 'actually infinite' set. Contrary to popular opinion
> >>>>> around here, there is room for both tools.
> >>>>
> >>>> Who here does not accept the validity of potentially infinite processes?
> >>>>
> >>>> There is one poster who talks about "potentially infinite sets" but they
> >>>> have crazy theorems (well, conjectures actually since no proofs have
> >>>> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
> >>>>
> >>>> Do you think there is also room for potentially infinite /sets/ here?
> >>>> If so, can you give an example of a theorem about them (with proof) that
> >>>> shows how they are different to the usual infinite sets?
> >>>
> >>> I have mentioned previously something very close.
> >>>
> >>> Studying the mathematical (set theoretical) structure of computer
> >>> viruses with the instruction set, the set of states, the set of
> >>> symbols, the number of heads, number of tapes, on a suitable stored
> >>> program random access machine with attached background storage. All
> >>> sets are finite except for the tape. I was introduced to the concept
> >>> of a 'semi-infinite' tape which was explained to be "as big as it
> >>> needs to be" and not to worry too much about it.
> >>
> >> We were taught "unbounded" rather than infinite.
> >> Semi-infinite I don't approve of, as it implies it has one bound.
> >> 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/
> >
> > Like, "the upper half-plane"?
> Reminds of a half plane to disc conformal mapping.
> >
> > I think it usually means "half the infinite" (i.e. in terms of symmetry and the unbounded).
> >

These days I've been trying to figure out octant-to-quadrant conformal mapping.
Like, just for positive numbers, in x and y, there's x=y, so the quadrants' two octants,
then for example drawing and converting curves their functions, to either
"negative in x" or "negative in y", and, ..., either when it starts flipping,
conformally mapping the quadrants to octants.

I've been looking at a lot going on with treating "x=y" as the axis, and the x and y
axis about ordinates and abscissae, and functions symmetrical about x=y, and
calling that the "identity dimension", and making for coordinates in it.
Also it's real trivial and singular and like 0 in "Clairaut" and "d'Alembert"
and like "linear fractional equations" or the "linear fractional transform"..

It's kind of easier to make it into a multi-dimensional analog
when it also looks like x=y=z. ("Roots of zero", "roots of the identity dimension").

Then the idea is kind of like that the hyperbola (y = 1/x) is pretty cool
about it, about "singularity analysis" and "singularities: not just
infinity anymore".

The field of mathematics has recently received important
new contributions. Rossy Boy and Jeniffer are at the forefront
of a new break through in the miracles of truth.

By the introduction of Quantifier Disambiguiation and point
seeing, thats the mathematical field when you eat
tons of cocaine and have keyboard access to google groups,

they are revolutionizing the world of science, as nobody else has ever done..

Ross Finlayson schrieb am Freitag, 2. Juni 2023 um 07:37:15 UTC+2:
> On Thursday, June 1, 2023 at 6:30:52 PM UTC-7, Chris M. Thomasson wrote:
> > On 6/1/2023 6:15 PM, Ross Finlayson wrote:
> > > On Thursday, June 1, 2023 at 12:22:44 PM UTC-7, Phil Carmody wrote:
> > >> FromTheRafters <F...@nomail.afraid.org> writes:
> > >>> Ben Bacarisse pretended :
> > >>>> FredJeffries <fredje...@gmail.com> writes:
> > >>>>
> > >>>>> You have stumbled onto the difference between a 'potentially infinite'
> > >>>>> process and an 'actually infinite' set. Contrary to popular opinion
> > >>>>> around here, there is room for both tools.
> > >>>>
> > >>>> Who here does not accept the validity of potentially infinite processes?
> > >>>>
> > >>>> There is one poster who talks about "potentially infinite sets" but they
> > >>>> have crazy theorems (well, conjectures actually since no proofs have
> > >>>> been offered) like WMath's sets E and P with E in P and P \ {E} = P.
> > >>>>
> > >>>> Do you think there is also room for potentially infinite /sets/ here?
> > >>>> If so, can you give an example of a theorem about them (with proof) that
> > >>>> shows how they are different to the usual infinite sets?
> > >>>
> > >>> I have mentioned previously something very close.
> > >>>
> > >>> Studying the mathematical (set theoretical) structure of computer
> > >>> viruses with the instruction set, the set of states, the set of
> > >>> symbols, the number of heads, number of tapes, on a suitable stored
> > >>> program random access machine with attached background storage. All
> > >>> sets are finite except for the tape. I was introduced to the concept
> > >>> of a 'semi-infinite' tape which was explained to be "as big as it
> > >>> needs to be" and not to worry too much about it.
> > >>
> > >> We were taught "unbounded" rather than infinite.
> > >> Semi-infinite I don't approve of, as it implies it has one bound.
> > >> 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/
> > >
> > > Like, "the upper half-plane"?
> > Reminds of a half plane to disc conformal mapping.
> > >
> > > I think it usually means "half the infinite" (i.e. in terms of symmetry and the unbounded).
> > >
> These days I've been trying to figure out octant-to-quadrant conformal mapping.
> Like, just for positive numbers, in x and y, there's x=y, so the quadrants' two octants,
> then for example drawing and converting curves their functions, to either
> "negative in x" or "negative in y", and, ..., either when it starts flipping,
> conformally mapping the quadrants to octants.
>
> I've been looking at a lot going on with treating "x=y" as the axis, and the x and y
> axis about ordinates and abscissae, and functions symmetrical about x=y, and
> calling that the "identity dimension", and making for coordinates in it.
> Also it's real trivial and singular and like 0 in "Clairaut" and "d'Alembert"
> and like "linear fractional equations" or the "linear fractional transform".
>
> It's kind of easier to make it into a multi-dimensional analog
> when it also looks like x=y=z. ("Roots of zero", "roots of the identity dimension").
>
> Then the idea is kind of like that the hyperbola (y = 1/x) is pretty cool
> about it, about "singularity analysis" and "singularities: not just
> infinity anymore".