Re: Fwd: SUO Quo Vadis
Phil,
Yes, I agree:
> Of course this depends on what "describe" means. The
> phrase "the real numbers" describes all the real numbers,
> not just a countable subset.
I was using the word "describe" to continue the terminology
that Avril adopted. I should have used the word "specify"
or "identify" to indicate that there is no finite statement
that can pick out a particular x out of an uncountable set
-- except for our familiar examples of pi, e, the solutions
to algebraic equations (such as the square root of 2), etc.
But there is a way to make the point using the word "describe":
For almost all real numbers x, there is no finite statement
S(x) that can describe x in a way that distinguishes x from
infinitely many other real numbers for which S is also true.
(The term "almost all" means all but a countable subset.)
John