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The Logic behind Cantor's PS proof!
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Graham Cooper
May 4, 2013, 3:07:35 AM5/4/13
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THERE EXISTS A POWERSET
OF THE INFINITE SET
WHICH IS BIGGER THAN THAT SET
FINITE OR OTHERWISE....
-----------------
Why is it BIGGER?
Say you list all the subsets of N, and
the 3rd subset does not contain 3.
Then you make a NEW SUBSET OF N
with a 3 in it, and then that new subset
can't be the 3rd subset! Can it?
No because see paragraph above...
Vice Versa, say the 3rd subset has a 3 in it,
then make the NEW SUBSET OF N miss a 3,
and then that new subset still can't be the 3rd subset
since 3 ~e 3rd subset.
So this new subset contains 1 IFF 1 ~e 1st subset
which means it can't be the 1st subset...
or the 2nd subset,
or the 3rd subset,..
So this NEW SUBSET isn't listed!
Since there are INF subsets
AND STILL MORE TO GO
The complete | POWERSET(N) | > |N|
This is how the REAL NUMBER SYSTEM WORKS!!
Herc
OF THE INFINITE SET
WHICH IS BIGGER THAN THAT SET
FINITE OR OTHERWISE....
-----------------
Why is it BIGGER?
Say you list all the subsets of N, and
the 3rd subset does not contain 3.
Then you make a NEW SUBSET OF N
with a 3 in it, and then that new subset
can't be the 3rd subset! Can it?
No because see paragraph above...
Vice Versa, say the 3rd subset has a 3 in it,
then make the NEW SUBSET OF N miss a 3,
and then that new subset still can't be the 3rd subset
since 3 ~e 3rd subset.
So this new subset contains 1 IFF 1 ~e 1st subset
which means it can't be the 1st subset...
or the 2nd subset,
or the 3rd subset,..
So this NEW SUBSET isn't listed!
Since there are INF subsets
AND STILL MORE TO GO
The complete | POWERSET(N) | > |N|
This is how the REAL NUMBER SYSTEM WORKS!!
Herc
Graham Cooper
May 5, 2013, 10:30:34 PM5/5/13
to
On May 6, 2:08 am, Newberry <newberr...@gmail.com> wrote:
> It does not. Suppose we define P(N) as the set of all the finite subsets of N. Then the real the numbers are infinite sequences of the elements of P(N).
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Do you get this far?
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Do you get this far?
me
May 6, 2013, 12:27:57 PM5/6/13
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Curlytop
May 7, 2013, 3:22:43 PM5/7/13
to
Graham Cooper set the following eddies spiralling through the space-time
continuum:
> Say you list all the subsets of N, and
> the 3rd subset does not contain 3.
>
> Then you make a NEW SUBSET OF N
> with a 3 in it, and then that new subset
> can't be the 3rd subset! Can it?
> No because see paragraph above...
No it's some other subset, possibly an infinite-numbered one.
--
ξ: ) Proud to be curly
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continuum:
> Say you list all the subsets of N, and
> the 3rd subset does not contain 3.
>
> Then you make a NEW SUBSET OF N
> with a 3 in it, and then that new subset
> can't be the 3rd subset! Can it?
> No because see paragraph above...
--
ξ: ) Proud to be curly
Interchange the alphabetic letter groups to reply
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