On Tuesday, December 3, 2013 9:09:53 AM UTC, WM wrote:
> This is the starting point of Cantor's first proof and all its variants: Let a sequence be gicen. With this assumption the limit is given as a defined number. To waste all naturals for the enumeration of the terms of the sequence is a very simple trick. Not convincing. |N could even be wasted for half of the terms. Or, after one sequence has been enumerated, the existence of further sequences could be used as a "proof" of uncountable sets.
Shouldn't really replying at all? I posted because it looked like you didn't understand what a "proof by contradiction" is. But then it seems you really don't understand what "proof by contradicting" is. "Zeit Geist"s fine post proved that the real numbers are uncountable by starting with an assumption that there is a sequence containing them all (which is _by definition_ the opposite of the reals being uncountable) and went on to demonstrate a contradiction, which means the assumption of the existence of such a sequence must be false.
You seem to object to the existence of such a sequence - not realising that this is _exactly_ the point. Except that I can't make any sense of your reasoning why you object, unlike Zeit Geist's original post which gives a very clear argument.