# Re: Infinities, cardinality, diagonalisation

But then I have another question, N is usually said to contains positive integer number from 0 to +infinity... but then it seems it should contains infinite length integer number... but then you enter the problem I've shown, so N shouldn't contains infinite length positive integer number. But if they aren't natural number then as the set seems uncountable they are in fact real number, but real number have a decimal point no ? so how N is restricted to only finite length number (the set is also infinite) without infinite length number ?

Thanks,
Quentin

On 7/13/06, Tom Caylor <[EMAIL PROTECTED]> wrote:

I think my easy answer is to say that infinite numbers are not in N.  I
like to think of it with a decimal point in front, to form a number
between 0 and 1.  Yes you have the rational numbers which eventually
have a repeating pattern (or stop).  But you also have in among them
the irrational numbers which are uncountable. (Hey this reminds me of
the fi among the Fi.)

To ask what is the next number after an infinite number, like
11111...11111... is similar asking what is the next real number after
0.11111...11111...

Tom

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