Re: An uncountable countable set

In article <virgil-8D882D.13064304092006@xxxxxxxxxxxxxxxxxxxxxx> Virgil <virgil@xxxxxxxxxxx> writes:
In article <1157367096.604428.36330@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:

But if you wish, provide a definition of "number". As far as I know,
there is not one in mathematics.

A number has only one of the following properties: It is larger than or
smaller than or equal to any natural number.

A complex number is a number which need not have any of these properties.

And before one uses "larger", "smaller" or "equal", in any definition,
one must define them too.

Moreover, I see now it is also badly worded. As it stands, I think,
are only three properties listed:
(1) larger than any natural number
(2) smaller than any natural number
(3) equal to any natural number.
And a number should satisfy only one of them. Question, is 3 a number?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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