> On 9 Jan., 17:01, Alan Smaill <sma...@SPAMinf.ed.ac.uk> 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 reals.
> In standard set theory it is > accepted.
So what? We're talking about WMathematics here, which grows murkier by the day.