PROOF INFINITY DOES NOT EXIST! Not even ONE type [Logic]

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From: George Greene on 10 Jul 2010 11:41

On Jul 9, 6:38 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> Perhaps you don't understand the proof, it only contradicts a well used axiom, not a well established fact.
>
> A REVISED PROOF OF THE NON-EXISTENCE OF INFINITY
>
> C10 = 0.12345678910111213141516...
>
> x = the number of digits in the expansion of C10

This can't be a proof of the non-existence of infinity,
because you are already asserting
that x IS infinity!!

> y = the number of consecutive digits of PI in C10

And now, this can't be a proof of anything, because y
DOES NOT EXIST!!!

> As x->oo, y->oo
NO,
DUMBASS, as
*h* approaches infinity, where h is A numeric digit-POSITION within
C10,
Y(H), NOT Y, i.e., the length of the longest prefix of Pi in the
length-h PREFIX of C10,
approaches infinity. BUT IT NEVER *GETS* THERE!

> x = oo

Yes, x=oo, BUT H, which is WHAT MATTERS, NEVER equals infinity --
it never even approaches it, frankly -- since ALL values of h ARE
ALWAYS INFINITELY
SMALLER than infinity, h always stays infinitely far away from
infinity, and only finitely
far from zero.

> Assume the limit exists.

WE CAN'T do this because you haven't said what "the limit" IS!!

> y=oo

> Contradiction (for each finite starting digit of PI in C10 there is a finite ending digit)

That IS NOT a contradiction, DUMBASS!
The fact that there is a finite ending digit for every prefix of Pi in
C10 does NOT imply
that THE LIMIT ALSO HAS that property!
If you consider the sequence
{1/2,3/4,7/8,15/16,31/32,63/64,127/128,255/256,511/512,1023/1024,2047/2048,etc},
then EVERY element of the sequence is LESS than1, but the limit IS
NOT less than 1! The limit EQUALS 1!
The fact that every element of some sequence has a property does NOT
imply that the limit ALSO has the property!
THAT is NOT what INDUCTION says or MEANS!!!
> Limit doesn't exist.

> y cannot reach infinity
> therefore x cannot reach infinity

It is entirely true that y cannot reach infinity and therefore h
cannot reach infinity.
That does NOT stop the LIMIT from being infinity! Limit operations
are read
"as x APPROACHES infinity" -- they DON'T SAY anything about what
happens
if x REACHES infinity, BECAUSE IT CAN'T!! THAT'S THE WHOLE POINT!

From: Wolf K on 10 Jul 2010 12:26

On 09/07/2010 18:42, |-|ercules wrote:
[...]
>
> You have a point for once. Early definitions of formal systems were
> "void of semantics".

Historically false. The realsiation that formal languages have no
content was arrived at over a period of centuries, and even today most
people can't grasp the concept.

[...]

wolf k.

From: Wolf K on 10 Jul 2010 12:28

On 09/07/2010 18:38, |-|ercules wrote:
> Perhaps you don't understand the proof, it only contradicts a well used
> axiom, not a well established fact.
>
>
>
>
> A REVISED PROOF OF THE NON-EXISTENCE OF INFINITY
>
>
> C10 = 0.12345678910111213141516...
>
> x = the number of digits in the expansion of C10
> y = the number of consecutive digits of PI in C10
>
> As x->oo, y->oo
> x = oo
>
> Assume the limit exists.
> y=oo
> Contradiction (for each finite starting digit of PI in C10 there is a
> finite ending digit)
> Limit doesn't exist.
>
> y cannot reach infinity
> therefore x cannot reach infinity
>
> x = the number of digits in the expansion of C10
> x =/= oo
>
> INFERENCE there is no oo
>
>
>
> Herc

Infinity is not a limit.

wolf k.

From: Wolf K on 10 Jul 2010 12:31

On 09/07/2010 16:46, George Greene wrote:
> On Jul 7, 2:31 pm, Aatu Koskensilta<aatu.koskensi...(a)uta.fi> wrote:
>> c...(a)kcwc.com (Curt Welch) writes:
>>> But math isn't about simple physical existence. It's about words and
>>> their definitions. It's a study of formal langauge and what can be
>>> _said_ using a formal language.
>>
>> No it's not.
>
> I wouldn't've been that simplistic about it, but I'll take your side
> on this,
> even though I usually defend that math is formal. NOTHING CAN be said
> with a formal language. That's THE WHOLE POINT; it's FORMAL.
> It doesn't MEAN ANYthing. It doesn't even NEED to mean anything.
> To the extent that math DOES mean something, there is more going on
> than "formal language".
> ANYthing "can" be said using a formal language, once you admit the
> possibility that formal languages
> can say things. You can just stipulate (don't ask ME how -- the SAME
> way the DICTIONARY does it;
> THAT'S how) -- that this or that formal gibberish MEANS whatever.
>

The dictionary records what the dictionary maker figures people mean
when they use words. The dictionary doesn't stipulate anything, even
though many people (still dazed by the nonsense passed off as "grammar
in grade 6) believe that the dictionary tells you waht words "really" mean.

cheers,
wolf k

From: K_h on 10 Jul 2010 16:41

"Nam Nguyen" <namducnguyen(a)shaw.ca> wrote in message
news:MTSZn.2663$Bh2.125(a)newsfe04.iad...
> K_h wrote:
>> "Curt Welch" <curt(a)kcwc.com> wrote in message
>> news:20100708093928.442$LY(a)newsreader.com...
>>> "|-|ercules" <radgray123(a)yahoo.com> wrote:
>>>> "Curt Welch" <curt(a)kcwc.com> wrote...
>>>> I realize the difficulty in confirming a rock exists. But all you have
>>>> to do is confirm *something* exists. Even if you're in error the
>>>> conclusion is still true. E x
>>>>
>>>> Herc
>>> That's an interesting point. I don't see any argument against the idea
>>> that something exists is an absolute truth. I think therefore I am. That
>>> might be the one and only absolute truth.
>>
>> Mathematical truth exists.
>
> Sure. In your mind for example!

And also outside of the human mind.

>> To my recollection, I have never seen anybody claim that 2x7=14 is false or
>> fails to be true after somebody dies.
>
> How did you mean by that? Did you mean the dead couldn't claim
> 2x7=14 is false? (If so, there are many things they couldn't
> possibly claim, naturally!)

No. Say your father dies and you are standing by his grave. Do you then claim
that 2x7=14 is now falsified?

>> The equation 10+20=30 is an absolute truth and that truth does exist.
>
> Again, in your mind perhaps. Others working in modulo arithmetic
> may state 10+20=0 is absolutely true, just as you stated "10+20=30
> is an absolute truth". What's the difference anyway?

If you don't believe that 10+20=30 is true in regular arithmetic then there's not
much point in arguing it. Obviously I was not referring to modulo arithmetic.

>> So you have existential doubts about the truth of 4+5=9?
>
> People have no doubt that 4+5=9 is false in some modulo arithmetic.

So we agree that there are absolute truths in both regular and modulo arithmetic.
In regular arithmetic 4+5=9 is true but Curt was claiming that there is some tiny
chance it could be wrong in regular arithmetic. Curt is obviously wrong there.

_