On 2010-06-17, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > I hate to disagree with you, because we are on much the same "side", but > this is not correct. Cantor's proof shows that you cannot form a list of all > Reals. This is not the same as the Reals being uncountable.
An infinite list of reals is just a function from N to R. Cantor's proof shows that no such function is surjective (and so in particular, not bijective). That is *exactly* the same as the Reals being uncountable.
> You can use Cantor's diagonal construction to similarly prove that you > cannot form a list of all computable numbers.
No, you can use something like Cantor's diagonal construction to similarly prove that you cannot form a *computable* list of all computable numbers. The qualifier is necessary to the proof.
