Re: Cantor Confusion


Han de Bruijn schrieb:

William Hughes wrote:

Tony Orlow wrote:

Well, the proof is simple. Any finite number of subdivisions of any
finite interval will only identify a finite number of real midpoints in
that interval, between any two of which will remain more real midpoints.
Therefore, there are more than any finite number of real points in the
interval.

This just shows that the number of real points is unbounded.
It does not show it is infinite (unless of course you use the
fact that any unbounded set of natural numbers is infinite).

Isn't unbounded the same as infinite, i.e. = not finite = unlimited =
without a limit?

Unbounded is potentially infinite but it is not necessarily actually
infinite.

Regards, WM

.

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