Re: Real Number --- Merely numbers whose digits can be infinitely long

On 02/05/2024 05:52, Ross Finlayson wrote:
[...]
[Keith:]

Or are you assuming that real numbers already exist, and you're defining
this notation on top of that?  If so, what's the point?

[Wij:]

Your request is valid but not practically reasonable.

Yet without an answer to that request, this whole discussion is
pointless.  We have been given a start towards a notation [which is not
new, people have been writing numbers using strings of digits "forever"]
with no reason given for why we should pay attention.  Except as a
diversion from endless debates about "halting".

I've found there's at least three definitions of real numbers,
Aristotle's first, Aristotle's second, and Fourier's. [...]

And the rest.  But every [sensible] new definition has come with
/either/ a proof that it is equivalent to an old definition, /or/ some
reason why it gives rise to a different collection of numbers [which is
then designated by some other name, to avoid confusion].  Wij refuses to
elaborate on his motivation, apart from apparently having some problem
with notions of limits.  He's not alone in that!
--
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Belliss