3 ms·
Not the comment-er, but here's a rough sketch. Definition: A computable number is a real number x such that there exists a total computable function f:Q->Q for
by alexbecker 12y ago
Not the comment-er, but here's a rough sketch.
Definition: A computable number is a real number x such that there exists a total computable function f:Q->Q for which, given any r>0, f(r) is within r of x.
Proof: There are only countably many total computable functions, since each can be described as a finite string of symbols from a finite alphabet. Hence only countably many computable numbers.