Re: Infinities, cardinality, diagonalisation

From: Quentin Anciaux <>
Date: Thu, 13 Jul 2006 15:29:19 +0200

Hi, thank you for your answer.

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 ?


On 7/13/06, Tom Caylor <> 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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Received on Thu Jul 13 2006 - 09:30:21 PDT

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