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Topic: The Distinguishability argument of the Reals.
Replies: 1   Last Post: Jan 9, 2013 12:33 PM

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Alan Smaill

Posts: 1,103
Registered: 1/29/05
Re: The Distinguishability argument of the Reals.
Posted: Jan 9, 2013 12:33 PM
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WM <> writes:

> On 9 Jan., 17:01, Alan Smaill <> wrote:

>> > It would be countable if "countable" was a sensible notion. Everybody
>> > who believes that "countable" is a sensible notion and that the power
>> > set axiom is valid must think that every subset of a countable set
>> > exists and is countable.

>> Wrong: Brouwer did not think so, for one.

> Brouwer did not think so because he denied uncountability.

That is simply irrelevant to your false claim.

> I said "everybody who believes that the power set axiom is valid".
> That is tantamount with uncountably many subsets of |N.

Not according to Brouwer.

>> More importantly, for WMathematics, you make assertions about a
>> non-existent set: there is no such set of finitely defined reals.

> There is the set of all finite definitions (and the set of all
> languages). A finitely defined real is defined by one or more finite
> definitions. And I assume that a subset has not larger cardinality
> than its super set.

You are already talking about a non-existent set.

> You may deny that.

*You* deny that there is such a set as the set of all finitely defined

> In standard set theory it is
> accepted.

So what? We're talking about WMathematics here, which grows
murkier by the day.

> Regards, WM

Alan Smaill

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