On Thursday, August 26, 2021 at 5:38:15 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 22:17:49 UTC+2:
> > On Thursday, August 26, 2021 at 4:59:55 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 26. August 2021 um 21:46:18 UTC+2:
> >
> > >
> > > > ... both "identity of number" and "same number" are nonsense
> > > I prove that there are more rationals in the interval (1000, 1001] than Cantor enumerates.
> > Nope. Your "proof" is nonsense
> It is proven by the number of rationals in the first unit interval

Indeed, it is based on the nonsense term "number of rationals".

--
William Hughes

On Thursday, August 26, 2021 at 5:41:19 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
>
> > Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
> The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.

Nope.

--
William Hughes

On 8/26/2021 4:52 PM, WM wrote:
> Jim Burns schrieb
> am Donnerstag, 26. August 2021 um 22:43:41 UTC+2:

>> I can prove it exists, that thing I say exists.
>
> In an inconsistent theory everything can be proved.

If you can prove arithmetic is inconsistent, go ahead.
"Inconsistent result" and "unwanted result"
aren't the same thing.

> I can prove that Cantor enumerates half of all rationals
> in (0, 1].

You are making a nonsense claim. Not-even-wrong.

> Call their number X. And I can prove that there are also
> X rationals in every other interval.

So can I. So can many people.
That's why your claim about "half" is not-even-wrong.

On Thursday, August 26, 2021 at 5:41:19 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
>
> > Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
> The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.

Nope. Between any *element of the set U* and 0 there is a real number (which depends on the element) i.e. there is no element of U that is next to zero. You cannot put a real number between the *set U* and 0, i.e. the set U is next to 0.

--
William Hughes

On Thursday, August 26, 2021 at 10:17:49 PM UTC+2, William wrote:

> Terms like "number of elements", "same number", "identity of number" [...] are nonsense for sets with infinite cardinality.

No, they aren't, silly.

Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)

card(A) = card(B) iff A ~ B

=> same cardinal number; identical cardinal numbers.

On 8/26/2021 3:38 PM, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 22:17:49 UTC+2:
>> On Thursday, August 26, 2021 at 4:59:55 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 26. August 2021 um 21:46:18 UTC+2:
>>
>>>
>>>> ... both "identity of number" and "same number" are nonsense
>>> I prove that there are more rationals in the interval (1000, 1001] than Cantor enumerates.
>> Nope. Your "proof" is nonsense
>
> It is proven by the number of rationals in the first unit interval.

Wrong

>
>>> Why do you call this proof is nonsense?
>> Because it is based on trying to compare the "number of elements" of sets with infinite cardinality.
>
> That is usual in mathematics of infinite series.

Wrong

>
>> Terms like "number of elements", "same number", "identity of number", "more", "half", ad nauseum are nonsense for sets with infinite cardinality.
>
> That is wrong. Crdinality is nonsense.

Wrong

> It leads to McDuck's bankruptcy,

Wrong

> to the empty intersection of infinite endsegments, and to more silly results which are irrelevant for any application of mathematics.

Wrong

>
> You should ponder about that for some days and nights. Perhaps you will be able to understand that it is nonsense to find half of all rationals in the first unit interval.

Wrong. That is your results, and it is Wrong

> In particular because the existence of more rationals than Cantor finds in the interval (1000, 1001] can be proved by
> 1/1 + 1000, 1/2 + 1000, 2/1 + 1000, 1/3 + 1000, 3/1 + 1000, 1/4 + 1000, ...

Wrong, Cantor enumerats all rational numbers with his SIMPLE proof

>
> Regards, WM
>
>

*7 wrongs in one post ALL sentences by WM are wrong*.

the following Ants are involved;

59 Always Wrong Ants
60 Alzheimer Ants
58 Always Without Proof Ants
55 ALU ants missing bit carry
138 Ants that fake knowing Mathematics
157 Ants that attach Electrodes to Chickens

159 Ants that can't do proofs.
178 Ants that process and remove WM
172 Ants that intentionally Stink at Math
947 Spoof not Proof Ants
948 Spoof Ants that sell “Dark Numbers”

835 Processed Ants
836 Professor Ants Beyond Me
837 Prole Ants
838 Prolefeed Ants
839 Proletarii Ants
840 Proof of Absence Ants

On 8/26/2021 3:52 PM, WM wrote:
> Jim Burns schrieb am Donnerstag, 26. August 2021 um 22:43:41 UTC+2:
>
>> I can prove it exists, that thing I say exists.
>
> In an inconsistent theory everything can be proved.
>
> I can prove that Cantor enumerates half of all rationals in (0, 1].

Wrong. Cantor enumerates ALL rationals in (0, 1].

On 8/26/2021 4:35 PM, Greg Cunt wrote:
> On Thursday, August 26, 2021 at 10:17:49 PM UTC+2, William wrote:
>
>> Terms like "number of elements", "same number", "identity of number" [...] are nonsense for sets with infinite cardinality.
>
> No, they aren't, silly.
>
> Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)
>
> card(A) = card(B) iff A ~ B
>
> => same cardinal number; identical cardinal numbers.
>

https://math.libretexts.org/Under_Construction/Stalled/Additional_Discrete_Topics_(Dean)/Infinite_Sets_and_Cardinality

On 8/26/2021 4:41 PM, WM wrote:
> William schrieb
> am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:

>> Correct. There is no element of U closest to zero.
>> There is a gap between any *element of the set U* and zero.
>> There is no gap between the *set U* and 0.
>
> The points of the real line are immovable.
> No quantifier tricks are possible.
> If there is no gap between "all points" and zero,
> then there are points next to zero.

No, you have that backwards.

2 and 3 are next to each other _in the integers_
because _there are no integers between them_
Next to == gap

2 and 3 are NOT next to each other _in the rationals_
_because there ARE rationals between them_
no gap == not next to

Each unit fraction 1/k is not _next to_ 0
because 0 < 1/(k+1) < 1/k

Just as 2 is not _next to_ 3
because 2 < 2.5 < 3

----
The rationals, in their standard order, cannot be stepped
one-by-one from any rational to any other rational.
This is equivalent to
no rational is _next to_ any other rational.

This is the opposite of how it is with naturals.
This is not a contradiction, it is a different description
of different things, rationals v. naturals.

On 8/26/2021 3:41 PM, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
>
>> Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
>
> The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.
>
> Regards, WM
>

you need to accept this fact, *there are no points 'next to' zero*.

Math Proof;

assume k is next to zero
however k/2 is closer to zero than k is
therefore the assumption is wrong
therfore there is no number "next to" zero.

WM, re read the math proof several times, let it sink in

(realize there are no numbers, "next to", other numbers EXCEPT in the case of open set. Which sounds the DEATH null to your "next to" there is no such
thing)

William schrieb am Donnerstag, 26. August 2021 um 23:12:08 UTC+2:
> On Thursday, August 26, 2021 at 5:38:15 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 26. August 2021 um 22:17:49 UTC+2:

> > It is proven by the number of rationals in the first unit interval
> Indeed, it is based on the nonsense term "number of rationals".
>
If we have an infinite matrix (like in the first diagonal argument) or plane, then its entries or points above the diagonal are precisely as many as below. You have to deny this simple truth in order to maintain Cantor's nonsense. This shows every impartial reader that you have a blocked brain.

Regards, WM

Jim Burns schrieb am Donnerstag, 26. August 2021 um 23:17:48 UTC+2:
> On 8/26/2021 4:52 PM, WM wrote:

> >> I can prove it exists, that thing I say exists.
> >
> > In an inconsistent theory everything can be proved.
> If you can prove arithmetic is inconsistent, go ahead.

Arithmetic is consistent. Set theory is inconsistent because if we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below. This shows that Cantor's enumeration is incomplete, no bijection, no valid measure of infinite sets.

> "Inconsistent result" and "unwanted result"
> aren't the same thing.

Unwanted is the result that in an infinite matrix or plane, the entries or points above the diagonal are precisely as many as below. That is basic and consistent.
> > I can prove that Cantor enumerates half of all rationals
> > in (0, 1].
> You are making a nonsense claim. Not-even-wrong.

This shows to every impartial reader that you have a blocked brain.

> > Call their number X. And I can prove that there are also
> > X rationals in every other interval.
> So can I. So can many people.

But not Cantor. He cannot even index one fraction of every unit interval because then he would run out of indexes. Would he really enumerate all rationals, he could start with all natnumbers. The set would not grow if the fractions n/1 would be taken before every other fraction. Or d you believe that reordering changes the size of the set?
> That's why your claim about "half" is not-even-wrong.

Half is what Cantor enumerates. The matrix of the first diagonal argument shows it irrefutably. Have a look here https://en.wikipedia.org/wiki/File:Diagonal_argument.svg if you dare it.

Regards, WM

William schrieb am Donnerstag, 26. August 2021 um 23:28:50 UTC+2:
> On Thursday, August 26, 2021 at 5:41:19 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
> >
> > > Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
> > The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.
> Nope. Between any *element of the set U* and 0 there is a real number (which depends on the element) i.e. there is no element of U that is next to zero. You cannot put a real number between the *set U* and 0, i.e. the set U is next to 0.

If they all are there, why not take the last one that is there?

Regards, WM

Greg Cunt schrieb am Donnerstag, 26. August 2021 um 23:35:51 UTC+2:

> Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)
>
Fact: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below.

That is independent of an attempted bijection. You have to deny this simple truth in order to maintain Cantor's nonsense. This shows every impartial reader that you have a blocked brain.

Regards, WM

Jim Burns schrieb am Freitag, 27. August 2021 um 00:20:04 UTC+2:

> Each unit fraction 1/k is not _next to_ 0
> because 0 < 1/(k+1) < 1/k

The cursor moving from 0 to 1 will encounter some unit fraction first.
>
> The rationals, in their standard order, cannot be stepped
> one-by-one from any rational to any other rational.
> This is equivalent to
> no rational is _next to_ any other rational.

The reason is that between two definble rationals, there are dark points. Same with the cursor. The unit fraction encountered first need not remain the smallest definable unit fraction. Smaller can be defined or found. But it is impossible to find all unit fractions, because only potentially infinitely many can be found. Almost all are dark and remain so.
>
> This is the opposite of how it is with naturals.

No, most natural are dark too. Beyond every defined natural there are aleph_0 dark naturals, almost all of which cannot become visible. All this explains your observation and rules. But you are not used to this explanation and by intellectual inertia you resist to consider it.

Regards, WM

On Friday, August 27, 2021 at 8:16:17 AM UTC-3, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 23:28:50 UTC+2:
> > On Thursday, August 26, 2021 at 5:41:19 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
> > >
> > > > Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
> > > The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.
> > Nope. Between any *element of the set U* and 0 there is a real number (which depends on the element) i.e. there is no element of U that is next to zero. You cannot put a real number between the *set U* and 0, i.e. the set U is next to 0.
> If they all are there, why not take the last one that is there?
>

Because while the set U contains many elements with the property they exist, it does not contain an element with the property that it is last. There is no "last one that is there". You cannot put a real number between the set U and 0.

--
William Hughes

William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
> On Friday, August 27, 2021 at 8:16:17 AM UTC-3, WM wrote:

> > If they all are there, why not take the last one that is there?
> >
> Because while the set U contains many elements with the property they exist, it does not contain an element with the property that it is last.

Nevertheless 0 has the property that all unit fractions come before it.

> There is no "last one that is there". You cannot put a real number between the set U and 0.

There is no real number between 0 and (0, 1]. That proves that the interval is next to 0, and since the interval is nothing but its points, the points of the interval are next to 0. But no point next to 0 can be found. Those next to zero are dark.

For every 1/n you can find 1/2n. A dark point has become visible. But almost all will remain forever dark.

Regards, WM

On 8/27/2021 7:45 AM, WM wrote:
> William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
>> On Friday, August 27, 2021 at 8:16:17 AM UTC-3, WM wrote:
>
>>> If they all are there, why not take the last one that is there?
>>>
>> Because while the set U contains many elements with the property they exist, it does not contain an element with the property that it is last.
>
> Nevertheless 0 has the property that all unit fractions come before it.
>
>> There is no "last one that is there". You cannot put a real number between the set U and 0.
>
> There is no real number between 0 and (0, 1].

that is what the notation means, 0 is excluded from the interval [0,1] by using (0,1]

> That proves that the interval is next to 0, and since the interval is nothing but its points,

the interval is a segment of the real line.

>the points of the interval are next to 0.

wrong. 0 is excluded from the interval [0,1] by using (0,1]
there are no points "next to" 0

> But no point next to 0 can be found. Those next to zero are dark.

wrong, there are no points "next to" 0

your dark points, or dark numbers are simply your way of explaining to yourself things you do not understand, it is dark to you.

>
> For every 1/n you can find 1/2n. A dark point has become visible. But almost all will remain forever dark.

you are lost again...

>
> Regards, WM
>

WM presented the following explanation :
> Greg Cunt schrieb am Donnerstag, 26. August 2021 um 23:35:51 UTC+2:
>
>> Hint: "In mathematics, the cardinality of a set is a measure of the "number
>> of elements" of the set." (Wikipedia, Cardinality)
>>
> Fact: If we have an infinite matrix or plane, then its entries or points
> above the diagonal are precisely as many as below.
>
> That is independent of an attempted bijection. You have to deny this simple
> truth in order to maintain Cantor's nonsense. This shows every impartial
> reader that you have a blocked brain.
>
> Regards, WM

Clearly there are four times as many integers as there are even
naturals in muckymath.

On 8/27/2021 6:16 AM, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 23:28:50 UTC+2:
>> On Thursday, August 26, 2021 at 5:41:19 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 26. August 2021 um 22:07:23 UTC+2:
>>>
>>>> Correct. There is no element of U closest to zero. There is a gap between any *element of the set U* and zero. There is no gap between the *set U* and 0.
>>> The points of the real line are immovable. No quantifier tricks are possible. If there is no gap between "all points" and zero, then there are points next to zero.
>> Nope. Between any *element of the set U* and 0 there is a real number (which depends on the element) i.e. there is no element of U that is next to zero. You cannot put a real number between the *set U* and 0, i.e. the set U is next to 0.
>
> If they all are there, why not take the last one that is there?
>
> Regards, WM
>

there is no 'last' one, no 'first' one, you should try to understand these basic things, it is holding you back.

your dark points, or dark numbers are simply your way of explaining to yourself things you do not understand, it is dark to you.

On 8/27/2021 6:27 AM, WM wrote:
> Jim Burns schrieb am Freitag, 27. August 2021 um 00:20:04 UTC+2:
>
>> Each unit fraction 1/k is not _next to_ 0
>> because 0 < 1/(k+1) < 1/k
>
> The cursor moving from 0 to 1 will encounter some unit fraction first.
>>
>> The rationals, in their standard order, cannot be stepped
>> one-by-one from any rational to any other rational.
>> This is equivalent to
>> no rational is _next to_ any other rational.
>
> The reason is that between two definble rationals, there are dark points. Same with the cursor. The unit fraction encountered first need not remain the smallest definable unit fraction. Smaller can be defined or found. But it is impossible to find all unit fractions, because only potentially infinitely many can be found. Almost all are dark and remain so.

wrong, the Cursor illuminates, defines, instantates ALL numbers without exception as it moves across, there are no dark numbers anywhere.

>>
>> This is the opposite of how it is with naturals.
>
> No, most natural are dark too. Beyond every defined natural there are aleph_0 dark naturals, almost all of which cannot become visible. All this explains your observation and rules.

Wrong. Fail.

>
> Regards, WM
>

your dark points, or dark numbers are simply your way of explaining to yourself things you do not understand, it is dark to you.

On 8/27/2021 6:04 AM, WM wrote:
> William schrieb am Donnerstag, 26. August 2021 um 23:12:08 UTC+2:
>> On Thursday, August 26, 2021 at 5:38:15 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 26. August 2021 um 22:17:49 UTC+2:
>
>>> It is proven by the number of rationals in the first unit interval
>> Indeed, it is based on the nonsense term "number of rationals".
>>
> If we have an infinite matrix (like in the first diagonal argument) or plane, then its entries or points above the diagonal are precisely as many as below. You have to deny this simple truth in order to maintain Cantor's nonsense. This shows every impartial reader that you have a blocked brain.
>
> Regards, WM
>

your conclusion is false.

On 8/27/2021 6:19 AM, WM wrote:
> Greg Cunt schrieb am Donnerstag, 26. August 2021 um 23:35:51 UTC+2:
>
>> Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)
>>
> Fact: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below.

show this in terms of math please. You are missing context.

What matrix ? What plane ?

what about the numbers on the diagonal ? Since you ignore them, you cannot conclude "precisely"

>
> That is independent of an attempted bijection. You have to deny this simple truth in order to maintain Cantor's nonsense.

what nonsense ? you are missing context.

> This shows every impartial reader that you have a blocked brain.

your dark points, or dark numbers are simply your way of explaining to yourself things you do not understand, it is dark to you.

>
> Regards, WM
>

On 8/27/2021 6:14 AM, WM wrote:
> Jim Burns schrieb am Donnerstag, 26. August 2021 um 23:17:48 UTC+2:
>> On 8/26/2021 4:52 PM, WM wrote:
>
>>>> I can prove it exists, that thing I say exists.
>>>
>>> In an inconsistent theory everything can be proved.
>> If you can prove arithmetic is inconsistent, go ahead.
>
> Arithmetic is consistent. Set theory is inconsistent

you think it is inconsistent, because you do not understand it.

>
>> "Inconsistent result" and "unwanted result"
>> aren't the same thing.
>
> Unwanted is the result that in an infinite matrix or plane, the entries or points above the diagonal are precisely as many as below. That is basic and consistent.
>>> I can prove that Cantor enumerates half of all rationals
>>> in (0, 1].
>> You are making a nonsense claim. Not-even-wrong.
>
> This shows to every impartial reader that you have a blocked brain.

your dark points, or dark numbers are simply your way of explaining to yourself things you do not understand, it is dark to you.

>
>>> Call their number X. And I can prove that there are also
>>> X rationals in every other interval.
>> So can I. So can many people.
>
> But not Cantor. He cannot even index one fraction of every unit interval because then he would run out of indexes.

wrong. you are still making 2 mistakes of assuming each iterval needs it own index, AND that one would run out of them.

you are straw grasping.

>Would he really enumerate all rationals, he could start with all natnumbers. The set would not grow if the fractions n/1 would be taken before every other fraction. Or d you believe that reordering changes the size of the set?

why is it so hard for you to understand the obvious and simple Cantor Enumeration ?

>
>> That's why your claim about "half" is not-even-wrong.
>
> Half is what Cantor enumerates. The matrix of the first diagonal argument shows it irrefutably. Have a look here https://en.wikipedia.org/wiki/File:Diagonal_argument.svg if you dare it.

wrong. Cantor enumerates all rationals.

>
> Regards, WM
>

Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
> Cantor enumerates all rationals.

Why doesn't he start with all fractions n/1?

Regards, WM