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Topic: When has countability been separted from listability?
Replies: 1   Last Post: Sep 30, 2017 2:41 PM

 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,394 Registered: 10/18/08
Re: When has countability been separted from listability?
Posted: Sep 30, 2017 2:41 PM

Am Samstag, 30. September 2017 20:05:54 UTC+2 schrieb John Gabriel:

> > That is correct. But it fails for the constructible real numbers.
>
> By constructible real number you mean compass and straight-edge construction?

I used the common definition https://en.wikipedia.org/wiki/Constructible_number
But we can also use very number that can be defined (of course by a finite set of letters).

> I do not consider these numbers. To me they are magnitudes. The measures of magnitudes are described by numbers. Such can neither be listed nor counted.

I think we can agree. A number has a magnitude or is related to a magnitude.

> > > I presume you use the binary or decimal tree to show that these "reals" in the set (0,1) are indeed countable?
> >
> > That is a way to show the countability of all real numbers. But for the constructible real numbers the not listability has been recognized by someone before us.

>
> Who?

I don't know who was the first.
>
> > That would have been the ultimate argument that set theory is nonsense. But set theorists appear to be unable even to remotely consider this possibility. It is easier to convince a stone of logic than a set theorist.
>
> :-)) Religion is a very strange thing. It wields an influence which is at most times beyond comprehension. Religion (faith) and logic (fact) do not mix.

That's why set theory and logic are separated by an abyss. But set theorists like to veil that lack by calling themselves logicans.

Regards, WM