Re: Cantor Confusion

In article <1165418973.725100.179680@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Franziska Neugebauer schrieb:

mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:
> Everybody knows what the number of ther EC states is.
[...]
The number of EC states is "the number of EC states".

This is hardly a definition.

It is simply a notion which can be equal to a natural number.

Which may evaluate to a number.

No. It evaluates to a number as little as 6 evaluates to a number. It
*is* a number, though not a fixed number. That is a matter of
definition of the word "number".


"Un-fixed numbers" are not numbers. They may be variables whose values
are niumbes, but they are not numbers.

Without explicitly or implicitly
providing a context (year) there is no definite answer in terms of
natural numbers. Mathematically the number of EC states can be modelled
as function of time.

The set of prime numbers does not contain the number 1.

According to a widespread defintion of "prime number" the set of prime
numers refers to a set which does not contain the number 1.

But once upon a time it did contain it.

There may have been a time, when a different set (one containing
the 1) was referred to by the named "set of prime numbers".

That is a matter of definition. It was *the* set of prime numbers.

Unless you specify a definition of primeness and a ring, that claim is
specious.

What constitutes the set of prime numbers depends on the definition of
prime numbers being used and the ring in which you are operating.
5 and 13 are not prime in the ring of Gaussian integers.

For any given definition of what is a prime, and in what ring it is to
be a prime, the set of primes is fixed and forever immutable.

Change either the definition or the ring, and you get may get a
different set. This is not a matter of time but of definition.
.

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