"Jesse F. Hughes" <je…@phiwumbda.org> wrote ..
- — -
> Herc7 <ozd…@australia.edu> writes:
>> On Jun 7, 6:56 pm, "Kelpie" <kelp…@gmail.com> wrote:
>>> "A Little Bit" <ti…@beerlover.com.au> wrote in messagenews:0l9p0696j5dql6jcuh953h1c4qg8teo6n3@4ax.com…
>>> > Adriana Xenides Dead of Wheel of Fortune fame has died after an operation
>>> > in hospital. She
>>> > was only 54.
>>> I hope she’s turning letters in the sky.
>> Xen dies
> X denies.
>> it appears I *have* disproven higher infinity
> No, you haven’t. The mysterious value X denies the validity of your
> "proof".
Fraid so, when I booted Ullrich out of my office due to Principal Transfer, the
reason I’m here, he forgot to take his little doggy with him, skit boy!
Funny nobody on sci.math will answer this question on higher infinity, on the same day
Xendies dies, a favorite Australian model who spent a career revealing what label was on the box!
>> Given a set of labeled boxes containing numbers inside them,
>> can you possibly find a box containing all the label numbers of boxes
>> that don’t contain their own label number?
Have a go mate!
Then if you’re the first sci.mather to admit I disproved Cantor, Halt, Turing, and Godel
in front of his peers you can be my Assistant Principal.
Herc
"|-|ercules" <radgray…@yahoo.com> writes:
>>> Given a set of labeled boxes containing numbers inside them,
>>> can you possibly find a box containing all the label numbers of boxes
>>> that don’t contain their own label number?
> Have a go mate!
The answer is no, near as I can figure.
Now, if you also knew that, for each set of numbers, there is a box
containing that set, then you’d have a paradox. Near as I can figure,
you *don’t* know that.
In set theory, on the other hand, we *do* know the analogous claim.
–
Jesse F. Hughes
"Casting [Demi] Moore as a woman who has come to the New World so that
she can ‘worship without fear or persecution’ in _The_Scarlet_Letter_
is like casting Bruce Willis as Young Rene Descartes." -Joe Queenan
"Jesse F. Hughes" <je…@phiwumbda.org> wrote
> "|-|ercules" <radgray…@yahoo.com> writes:
>>>> Given a set of labeled boxes containing numbers inside them,
>>>> can you possibly find a box containing all the label numbers of boxes
>>>> that don’t contain their own label number?
>> Have a go mate!
> The answer is no, near as I can figure.
> Now, if you also knew that, for each set of numbers, there is a box
> containing that set, then you’d have a paradox. Near as I can figure,
> you *don’t* know that.
> In set theory, on the other hand, we *do* know the analogous claim.
So, no box ever containing the numbers of boxes not containing their own numbers
means higher infinities exist?
Herc
"William Hughes" <wpihug…@hotmail.com> wrote ..
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> On Jun 7, 6:46 pm, "|-|ercules" <radgray…@yahoo.com> wrote:
>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>> > "|-|ercules" <radgray…@yahoo.com> writes:
>> >>>> Given a set of labeled boxes containing numbers inside them,
>> >>>> can you possibly find a box containing all the label numbers of boxes
>> >>>> that don’t contain their own label number?
>> >> Have a go mate!
>> > The answer is no, near as I can figure.
>> > Now, if you also knew that, for each set of numbers, there is a box
>> > containing that set, then you’d have a paradox. Near as I can figure,
>> > you *don’t* know that.
>> > In set theory, on the other hand, we *do* know the analogous claim.
>> So, no box ever containing the numbers of boxes not containing their own numbers
>> means higher infinities exist?
> Yes.
> – William Hughes
Good. After 4 days you’ve been given the OK by Ullrich’s sidekick to admit, err…
No box ever containing the numbers of boxes not containing their own number
means higher infinities exist.
Herc
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"|-|ercules" <radgray…@yahoo.com> writes:
> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>> "|-|ercules" <radgray…@yahoo.com> writes:
>>>>> Given a set of labeled boxes containing numbers inside them,
>>>>> can you possibly find a box containing all the label numbers of boxes
>>>>> that don’t contain their own label number?
>>> Have a go mate!
>> The answer is no, near as I can figure.
>> Now, if you also knew that, for each set of numbers, there is a box
>> containing that set, then you’d have a paradox. Near as I can figure,
>> you *don’t* know that.
>> In set theory, on the other hand, we *do* know the analogous claim.
> So, no box ever containing the numbers of boxes not containing their own numbers
> means higher infinities exist?
*Given* that every set of numbers is contained in some box, I guess
so.
But I don’t see how this analogy is supposed to make Cantor’s theorem
appear dubious.
–
Jesse F. Hughes
"Well, I’m a pragmatist. I’ve been wrong MANY TIMES and it seems to
me that it would be simpler to be wrong with this paper."
–James S. Harris explains his latest paper
"Jesse F. Hughes" <je…@phiwumbda.org> wrote
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> "|-|ercules" <radgray…@yahoo.com> writes:
>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>> "|-|ercules" <radgray…@yahoo.com> writes:
>>>>>> Given a set of labeled boxes containing numbers inside them,
>>>>>> can you possibly find a box containing all the label numbers of boxes
>>>>>> that don’t contain their own label number?
>>>> Have a go mate!
>>> The answer is no, near as I can figure.
>>> Now, if you also knew that, for each set of numbers, there is a box
>>> containing that set, then you’d have a paradox. Near as I can figure,
>>> you *don’t* know that.
>>> In set theory, on the other hand, we *do* know the analogous claim.
>> So, no box ever containing the numbers of boxes not containing their own numbers
>> means higher infinities exist?
> *Given* that every set of numbers is contained in some box, I guess
> so.
> But I don’t see how this analogy is supposed to make Cantor’s theorem
> appear dubious.
So, as many have put it, the holy grail of mathematics, the infinite paradise is based on
no box containing the numbers of boxes that don’t contain their own number?
Herc
> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>> But I don’t see how this analogy is supposed to make Cantor’s theorem
>> appear dubious.
What about this statement?
All possible digit sequences are computable to all, as in an infinite amount of, finite lengths.
Herc
On 2010-06-08, |-|ercules <radgray…@yahoo.com> wrote:
> What about this statement?
> All possible digit sequences are computable to all, as in an
> infinite amount of, finite lengths.
What about it? Apart from being an example of a mathematically
ambiguous statement with at least 3 reasonable interpretations, 2 of
which make it false and 1 makes it true, that is.
- Tim
|-|ercules says…
>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>> But I don’t see how this analogy is supposed to make Cantor’s theorem
>>> appear dubious.
>What about this statement?
>All possible digit sequences are computable to all, as in an infinite amount
>>of, finite lengths.
The correct statement is this:
I. For every real number r, for every natural number n, there
exists a computable real r’ such that r agrees with r’ in
the first n decimal places.
Note the logical form of this statement:
forall r, forall n, exists r’ …
The order of quantifiers makes a difference! If the change
the order of quantifiers we get a similar-looking but false
statement:
II. For every real number r, there exists a computable real r’,
for every natural number n:
r agrees with r’ in the first n decimal places.
This has the logical form:
forall r, exists r’, forall n, …
It differs from the first statement in that the order
of the quantifiers has been changed.
Statement I is true. Statement II is false. The claim that
"not all reals are computable" is equivalent to the claim
"Statement II is false". The diagonal argument proves that
Statement II is false, not that Statement I is false.
–
Daryl McCullough
Ithaca, NY
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"|-|ercules" <radgray…@yahoo.com> writes:
> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>> "|-|ercules" <radgray…@yahoo.com> writes:
>>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>>> "|-|ercules" <radgray…@yahoo.com> writes:
>>>>>>> Given a set of labeled boxes containing numbers inside them,
>>>>>>> can you possibly find a box containing all the label numbers of boxes
>>>>>>> that don’t contain their own label number?
>>>>> Have a go mate!
>>>> The answer is no, near as I can figure.
>>>> Now, if you also knew that, for each set of numbers, there is a box
>>>> containing that set, then you’d have a paradox. Near as I can figure,
>>>> you *don’t* know that.
>>>> In set theory, on the other hand, we *do* know the analogous claim.
>>> So, no box ever containing the numbers of boxes not containing their own numbers
>>> means higher infinities exist?
>> *Given* that every set of numbers is contained in some box, I guess
>> so.
>> But I don’t see how this analogy is supposed to make Cantor’s theorem
>> appear dubious.
> So, as many have put it, the holy grail of mathematics, the infinite
> paradise is based on no box containing the numbers of boxes that
> don’t contain their own number?
I wouldn’t call Cantor’s theorem a holy grail, nor claim that it is
*based on* your odd analogy, but in any case this discussion is pretty
pointless.
Your analogy does not refute the simple fact: Cantor’s theorem is a
theorem of ZF.
–
Jesse F. Hughes
"Mistakes are big part of the discovery process.
I make lots of them. Kind of pride myself on it."
— James S. Harris
On 2010-06-08, Daryl McCullough <stevendaryl3…@yahoo.com> wrote:
> Note the logical form of this statement:
> forall r, forall n, exists r’ …
> The order of quantifiers makes a difference! If the change
> the order of quantifiers we get a similar-looking but false
> statement
I think you’re wasting your time. Like many cranks, Herc can’t now
and probably won’t ever be able to tell the difference.
- Tim
"Daryl McCullough" <stevendaryl3…@yahoo.com> wrote …
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> |-|ercules says…
>>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>>> But I don’t see how this analogy is supposed to make Cantor’s theorem
>>>> appear dubious.
>>What about this statement?
>>All possible digit sequences are computable to all, as in an infinite amount
>>>of, finite lengths.
> The correct statement is this:
> I. For every real number r, for every natural number n, there
> exists a computable real r’ such that r agrees with r’ in
> the first n decimal places.
> Note the logical form of this statement:
> forall r, forall n, exists r’ …
> The order of quantifiers makes a difference! If the change
> the order of quantifiers we get a similar-looking but false
> statement:
> II. For every real number r, there exists a computable real r’,
> for every natural number n:
> r agrees with r’ in the first n decimal places.
> This has the logical form:
> forall r, exists r’, forall n, …
> It differs from the first statement in that the order
> of the quantifiers has been changed.
> Statement I is true. Statement II is false. The claim that
> "not all reals are computable" is equivalent to the claim
> "Statement II is false". The diagonal argument proves that
> Statement II is false, not that Statement I is false.
Right, but statement 1 is sufficient to disprove that modifying the diagonal produces a new sequence of digits.
This is what a new sequence of digits looks like:
123
456
789
DIAG = 159
ANTIDIAG = 260
260 is a NEW SEQUENCE OF DIGITS.
WHERE is the new sequence of digits coming from when all possible digit sequences are computable to all, as in an infinite amount
of, finite lengths?
Herc
"Jesse F. Hughes" <je…@phiwumbda.org> wrote
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> "|-|ercules" <radgray…@yahoo.com> writes:
>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>> "|-|ercules" <radgray…@yahoo.com> writes:
>>>> "Jesse F. Hughes" <je…@phiwumbda.org> wrote
>>>>> "|-|ercules" <radgray…@yahoo.com> writes:
>>>>>>>> Given a set of labeled boxes containing numbers inside them,
>>>>>>>> can you possibly find a box containing all the label numbers of boxes
>>>>>>>> that don’t contain their own label number?
>>>>>> Have a go mate!
>>>>> The answer is no, near as I can figure.
>>>>> Now, if you also knew that, for each set of numbers, there is a box
>>>>> containing that set, then you’d have a paradox. Near as I can figure,
>>>>> you *don’t* know that.
>>>>> In set theory, on the other hand, we *do* know the analogous claim.
>>>> So, no box ever containing the numbers of boxes not containing their own numbers
>>>> means higher infinities exist?
>>> *Given* that every set of numbers is contained in some box, I guess
>>> so.
>>> But I don’t see how this analogy is supposed to make Cantor’s theorem
>>> appear dubious.
>> So, as many have put it, the holy grail of mathematics, the infinite
>> paradise is based on no box containing the numbers of boxes that
>> don’t contain their own number?
> I wouldn’t call Cantor’s theorem a holy grail, nor claim that it is
> *based on* your odd analogy, but in any case this discussion is pretty
> pointless.
> Your analogy does not refute the simple fact: Cantor’s theorem is a
> theorem of ZF.
What’s the deduction step in ZF that says "higher infinities exist".
Herc
On 2010-06-09, |-|ercules <radgray…@yahoo.com> wrote:
> Right, but statement 1 is sufficient to disprove that modifying the
> diagonal produces a new sequence of digits.
As predicted, Herc can’t understand the difference nor why it makes
nonsense of his claims.
> WHERE is the new sequence of digits coming from when all possible
> digit sequences are computable to all, as in an infinite amount of,
> finite lengths?
For *all* N, the sequence differs from the Nth entry in the list at
the Nth digit (and possibly other positions as well). It is new
because for *every* sequence in the list, the question "is it the same
as this sequence" is answered "no".
Unfortunately Herc really is dumb enough to think that with enough
"no" answers, it really means "yes".
- Tim
On 2010-06-09, |-|ercules <radgray…@yahoo.com> wrote:
> What’s the deduction step in ZF that says "higher infinities exist".
Herc is dumb enough to think that every proof in ZF consists of a
single deduction step, *the* step.
- Tim
"Tim Little" <t…@little-possums.net> wrote
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> On 2010-06-09, |-|ercules <radgray…@yahoo.com> wrote:
>> Right, but statement 1 is sufficient to disprove that modifying the
>> diagonal produces a new sequence of digits.
> As predicted, Herc can’t understand the difference nor why it makes
> nonsense of his claims.
>> WHERE is the new sequence of digits coming from when all possible
>> digit sequences are computable to all, as in an infinite amount of,
>> finite lengths?
> For *all* N, the sequence differs from the Nth entry in the list at
> the Nth digit (and possibly other positions as well). It is new
> because for *every* sequence in the list, the question "is it the same
> as this sequence" is answered "no".
So you think the antidiagonal comes up with an actual NEW SEQUENCE OF DIGITS
and this does not contradict that ALL sequences of digits are on the computable
list of reals up to all (an infinite amount of) digit positions?
Herc
On 2010-06-09, |-|ercules <radgray…@yahoo.com> wrote:
> So you think the antidiagonal comes up with an actual NEW SEQUENCE
> OF DIGITS and this does not contradict that ALL sequences of digits
> are on the computable list of reals up to all (an infinite amount
> of) digit positions?
Your question is incoherent, as it implies that every finite segment
being on the list is equivalent to the entire sequence being on the
list. The equivalence is false, so your question is meaningless.
To be more precise:
The statement "ALL sequences of digits are on the list of computable
reals up to all finite digit positions" is true.
The statement "ALL sequences of digits are on the list of computable
reals (to infinite digit positions)" is false.
Your question equates these statements. Perhaps you should focus on
this issue, as it seems to be the core of your inability to understand
Cantor’s proof.
As an aside, any list of all computable reals is not a computable
list, so your use of the term "the computable list of reals" is
incorrect in your context.
Finally, the introduction of computable reals is a red herring:
Cantor’s proof had nothing to do with computability.
- Tim
"Tim Little" <t…@little-possums.net> wrote …
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> On 2010-06-09, |-|ercules <radgray…@yahoo.com> wrote:
>> So you think the antidiagonal comes up with an actual NEW SEQUENCE
>> OF DIGITS and this does not contradict that ALL sequences of digits
>> are on the computable list of reals up to all (an infinite amount
>> of) digit positions?
> Your question is incoherent, as it implies that every finite segment
> being on the list is equivalent to the entire sequence being on the
> list. The equivalence is false, so your question is meaningless.
> To be more precise:
> The statement "ALL sequences of digits are on the list of computable
> reals up to all finite digit positions" is true.
> The statement "ALL sequences of digits are on the list of computable
> reals (to infinite digit positions)" is false.
> Your question equates these statements. Perhaps you should focus on
> this issue, as it seems to be the core of your inability to understand
> Cantor’s proof.
I don’t equate those statements, I merely substitute "all" with "infinite amount of".
How many natural numbers are there in "all natural numbers"?
Given that, do you still maintain you cannot parse this question?
>> So you think the antidiagonal comes up with an actual NEW SEQUENCE
>> OF DIGITS and this does not contradict that ALL sequences of digits
>> are on the computable list of reals up to all (an infinite amount
>> of) digit positions?
Herc
On 2010-06-10, |-|ercules <radgray…@yahoo.com> wrote:
> I don’t equate those statements, I merely substitute "all" with
> "infinite amount of".
Incorrectly so.
No sequence in the list has all its digits in common with the
antidiagonal. There may be some sequences in the list that have an
infinite amount of digits in common with the antidiagonal. For any
finite n there may also be sequences that agree to n places.
None of these descriptions are substitutable for each other.
More mathematically, let A be the antidiagonal and L be the list.
True: "For all n in N, there exists S in L such that S matches A to n
places".
False: "There exists S in L such that for all n in N, S matches A to n
places".
The former statement is a formalisation of "any finite number of
places" and the latter formalises "infinite amount of places".
You are treating the two statements as equivalent, which is why some
people are saying you have quantifier dyslexia. They differ only in
the ordering of the quantifiers.
> Given that, do you still maintain you cannot parse this question?
The question can be parsed, but it includes a counterfactual premise
and so is ill-posed.
You seem to like analogies, so here is one: Your repetition of your
ill-posed question is a mathematical equivalent of saying
"Is the elephant in your refrigerator green or yellow? STOP DODGING
THE QUESTION AND ANSWER GREEN OR YELLOW!"
when the truth is simply that there is no such elephant and so any
question of its colour is meaningless.
Likewise your substitution of different terms as if they were
equivalent renders a YES/NO answer to your question meaningless. They
are not equivalent, and if you want a meaningful answer you need to
ask a meaningful question.
- Tim
"Tim Little" <t…@little-possums.net> wrote
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> On 2010-06-10, |-|ercules <radgray…@yahoo.com> wrote:
>> I don’t equate those statements, I merely substitute "all" with
>> "infinite amount of".
> Incorrectly so.
> No sequence in the list has all its digits in common with the
> antidiagonal. There may be some sequences in the list that have an
> infinite amount of digits in common with the antidiagonal. For any
> finite n there may also be sequences that agree to n places.
> None of these descriptions are substitutable for each other.
> More mathematically, let A be the antidiagonal and L be the list.
> True: "For all n in N, there exists S in L such that S matches A to n
> places".
> False: "There exists S in L such that for all n in N, S matches A to n
> places".
> The former statement is a formalisation of "any finite number of
> places" and the latter formalises "infinite amount of places".
> You are treating the two statements as equivalent, which is why some
> people are saying you have quantifier dyslexia. They differ only in
> the ordering of the quantifiers.
>> Given that, do you still maintain you cannot parse this question?
> The question can be parsed, but it includes a counterfactual premise
> and so is ill-posed.
> You seem to like analogies, so here is one: Your repetition of your
> ill-posed question is a mathematical equivalent of saying
> "Is the elephant in your refrigerator green or yellow? STOP DODGING
> THE QUESTION AND ANSWER GREEN OR YELLOW!"
> when the truth is simply that there is no such elephant and so any
> question of its colour is meaningless.
> Likewise your substitution of different terms as if they were
> equivalent renders a YES/NO answer to your question meaningless. They
> are not equivalent, and if you want a meaningful answer you need to
> ask a meaningful question.
> – Tim
I have little time for you as you keep snipping the points you refute then
repeating your exact same error.
Herc
On 2010-06-10, |-|ercules <radgray…@yahoo.com> wrote:
> I have little time for you as you keep snipping the points you
> refute then repeating your exact same error.
I’m not surprised that you have little time for me. By interacting
with me you run the risk of having to admit your errors to yourself,
and that would be abhorrent to you.
- Tim