Re: The natural numbers are uncountable

From: Poker Joker (Poker_at_wi.rr.com)
Date: 07/07/04 

Date: Wed, 07 Jul 2004 22:29:43 GMT

"Andrew" <stan370@btinternet.com> wrote in message
news:7zgGc.2341$Rt4.1117@newsfe5-win.ntli.net...
> Given any simply infinite sequence of unique natural numbers, regardless
of
> the specific identity of the natural number at each position in the
> sequence, there is first element in the sequence, a second element in the
> sequence, and so on, and so on, hence any simply infinite sequence of
unique
> natural numbers may be substituted for an infinite sequence of the natural
> numbers in their natural order (i.e., 1, 2, 3, . . .). Which must mean
that
> any such sequence is countable.

Then why is the subject: "The natural numbers are uncountable?" I assume
that you want to argue that the naturals are not countable, so why is this
your first argument? People who are convincing usually come out with their
strongest argument first. Is this the best you can do? Argue the wrong
side
of your own argument?

Relevant Pages

  • The Origin of a Sequence
    ... THE ORIGIN OF A SEQUENCE ... implications of the first part for the understanding of natural number as ... In mathematics, so far as I can tell, a sequence is always ... But let us go back to our idea of the Naturals ...
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  • Re: New countable infiniity logic
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  • Re: New countable infiniity logic
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  • Re: infinity
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  • Re: Continuum hypothesis
    ... > So you're saying that there exists an infinite sequence (i.e., ... > sense to talk about it as a mathematical object)? ... But the "standard" naturals seem to have ...
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