Virgil
Posts:
4,479
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 5, 2013 4:44 PM
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In article
<b7fc4126-ed54-4740-a873-0a64830621a0@h2g2000yqa.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Jan., 22:38, Virgil <vir...@ligriv.com> wrote:
>
> > According to standard mathematics, a set is "countable" if and only if
> > there is surjection from N to that set.
>
> If and only if? Do you agree that a subset of a countable set is
> countable?
Since a surjection from N to a superset of S trivially implies a
surjection to S, it also implies that any subset of a countable set is
also countable. at least outside of WMythology. What the rules are for
goes on inside or WMythology is only accessible to WM himself.
>
> The set of all finite definitions is countable.
> The set of all finitely defined reals cannot be put in bijection with |
> N, but it is a subset of all finite definitions, isn't it?
There is nothing in any definition of a complete ordered field of reals
that requires each of its members to be finitely definable.
At least not outside WMytheology.
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