Re: Ultimate debunking of Cantor's Theory

On Jul 13, 3:51 pm, Calvin <cri...@xxxxxxxxxxxxxx> wrote:
On Jul 13, 4:22 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

You cannot prove the existence of an actually infinte set.

You can't prove the existence of the infinite set N
of natural numbers? Of course you can, as follows:

Assume the contrary, that N is finite.

Nope. This is the mistake: You are assuming that N can be constructed
in the first place. In other words, how is Calvin's proof different
from the proof of the following "theorem"?

THEOREM. 1/0 is irrational.

Proof: Suppose 1/0 is a rational number p/q; that is, p and q are
integers, and q is nonzero. Then
1/0 = p/q means 1*q = p*0, or q = 0. This contradicts the condition
that q be nonzero. Hence the assumption is false; q/0 is not rational,
which means it's irrational. QED.

--- Christopher Heckman

It would then have
a largest element L, by the definition of N, which is that
it is comprised of the elements of the sequence 1, 2, 3, ...
(or if you prefer, 1, (1+1), (1+1+1), ...).

But for every n in N, n+1 is also a natural number.
Thus L+1 is a natural number, which contradicts
the assumption that L is the largest element of N.

Therefore the proposition that N is not infinite is
false.


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