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Topic: § 422 What is a definition of a number?
Replies: 53   Last Post: Jan 23, 2014 9:13 AM

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 mueckenh@rz.fh-augsburg.de Posts: 13,452 Registered: 1/29/05
Re: § 422 What is a definition of a number?
Posted: Jan 22, 2014 8:01 AM

On Wednesday, 22 January 2014 13:42:39 UTC+1, wpih...@gmail.com wrote:
> On Wednesday, January 22, 2014 5:21:58 AM UTC-4, muec...@rz.fh-augsburg.de wrote:
>
>
>

> >it can be proved in addition that the set of all infinite sequences of digits >is countable.
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>
>
> The collection of all infinite sequences is not a potentially infinite set
>
> (WM).

Here we are using set theory.

> Thus there cannot be a potentially infinite list of all
>
> infinite sequences (otherwise the collection of all infinite sequences
>
> would be a potentially infinite set). So the collection of all infinite
>
> sequences is unlistable.

Here we are proving that their cardinality is not larger than that of the countable set of all nodes.
>
>
>
> What do you mean by uncountable?
>

Nothing. It is nonsense. But here we are using set theory. There uncountable is larger than countable.

Regards, WM