Re: Cantor Confusion

In article <45746B98.5040606@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

On 12/1/2006 8:20 PM, Virgil wrote:
In article <1164967792.130794.251330@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

May be if you apply your personal definition of potentially infinity,
but not if you apply the generally accepted definition.

What "generally accepted" meaning is that? Most mathematicians do not
accept that a set can be "potentially" infinite without being actually
so.

I see it quite differently: Potentially and actually infinite points of
view mutually exclude each other as do countable and uncountable,
rational and irrational.

Except that countable and uncountable coexist within the same set theory
and rational and irrational coexist within the same real umber field.

But potentially infinite does not exist within ZF or NBG or NF or any
other standard set theory.
.

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