Talk:Fractions

I think the use/meaning of well-ordered, as it is used in the context of denumerability on this page, should be explained.

There is also something confusing in the description of this lexicographical order: "first according to |n|+d" makes sense, and also "secondly according to n", but the inequality -(|n|+d) < n < |n|+d does not really make sense: by definition of |.|, one always has -|n| ≤ n ≤ |n|, so yes, adding d ≥ 1 to |n| allows to go to the strict inequality, but that inequality is trivially satisfied for *any* n. What is meant, of couse, is that |n|+d is a constant, say N, and that n goes from -N+1 to N-1. I think the inequality should either be phrased like that (using a variable different from n for the bounds, and then maybe better use weak equalities ≤ to clarify that they give the initial and final value of n in that group), or could simply be dropped: n just goes from the largest negative to the largest positive numerator, among all fractions with fixed |n|+d. Maybe no need to say that these are given when d=1, namely -(|n|+d)+1 and |n|+d-1, respectively. — MFH 22:07, 8 December 2020 (EST)