Re: Cantor Confusion

On 12/5/2006 2:50 AM, *** T. Winter wrote:
In article <1165263838.656385.305770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> "MoeBlee" <jazzmobe@xxxxxxxxxxx> writes:
> Eckard Blumschein wrote:
> > Correct. There are people who extend the reals to include oo.
>
> Would you give an example of a text that does this?
>
> What we sometimes do is add two points (called 'oo' and '-oo') to the
> real number system so that we have a different, extended system (which
> is not a complete ordered field). But that does not meant that we
> consider oo and -oo to be real numbers.

In the one-point compactification of the real line or the complex plane
a single point at infinity is added. But also in that case it is either
a real nor a complex number. And again, the result is not a field, and
also not odered.

Obviously, you meant not either but neither?

I wonder why the mathematicians believe to require one-point
compactification. I consider the rationals as genuine numbers, being as
close as you like to the fictions infinity and real numbers. The exact
numerical representation of pi requires the fiction of actual infinity.

.

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