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Topic: Matheology 400: WM's Quantifier Confusion
Replies: 1   Last Post: Dec 11, 2013 5:58 AM

 Alan Smaill Posts: 1,103 Registered: 1/29/05
Re: Matheology 400: WM's Quantifier Confusion
Posted: Dec 11, 2013 5:58 AM

Virgil <virgil@ligriv.com> writes:

> WM <wolfgang.mueckenheim@hs-augsburg.de> wrote:
>

>> Am Dienstag, 10. Dezember 2013 14:01:30 UTC+1 schrieb wpih...@gmail.com:
>>

>
>> > Then you know that for a constructivist there is no list of
>> > all real numbers.

>
> For a constuctivist there is also no complete list of all rational
> numbers.

??

There's no problem in giving an effective function from |N to
the rationals. The intuitionist position is that the rationals
are therefore countable. (WM's claim to the contrary notwithstanding.)

There *is* a problem giving such a function from |N to the
computable reals.

>> Here we need a list of all rational numbers only.
>
> Which, other than for constructivists is easy enough.
>

>> This list can be diagonalized. The first few digits of the
>> antidiagonal cannot prove that the antidiagonal differs from all
>> rational numbers of the list.

>
> But a general rule, applied equally to all digit positions, can.

Exactly.

--
Alan Smaill