Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx wrote:
*** T. Winter schrieb:

That is especially not the
case when you consider only representations to some integral base.
There are other methods to define numbers. You do not like to call
them numbers, but ideas. But you can not prevent me to call something
like sqrt(2) a (real) number. And in common mathematics that is just
what it is.

By definition, every sequence (use any definition, I know Cantor,
Dedekind, Baudet and Weierstrass, they all lead to the same):
{sum{k = 1...n} a_k/10^k}
is a representative of a "number". It is just a sequence of rationals.

Therefore I do not understand why you say "Numbers are fixed entities".
They are merely defined by sequences.

OK, I'll bite: How does defining a number as a sequence contradict that
a number is a fixed entity?

--
David Marcus
.

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