Re: Cantor Confusion


*** T. Winter schrieb:


The balls in vase problem suffers because the problem is not well-defined.
Most people in the discussion assume some implicit definitions, well that
does not work as other people assume other definitions. How do you
*define* the number of balls at noon? You can not use limits, because the
limit does not exist when you use standard mathematics.

But we can safely say that lim{n-->oo}n = 0 is false.
lim{n-->oo}n can be estimated by lim{n-->oo} 1/n = 0.

So using standard
definitions there is no answer. More precise, given the sequence of sets:
{1, ..., 10)
{2, ..., 20}
{3, ..., 30}
etc., is there a limit? Well, no, there is no defined limit unless you
define what a limit of sets looks like. I have never seen a definition
that tells me how the limit of a sequence is defined. The limit of the
size of the sets also gives no answer, because that limit does not exist.
Strange enough, when somebody goes on to define things, *you* question his
definitions, rather than the result.

The limit {1,...,n} for n-->oo is N, if N does exist.

Regards, WM

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