5. Let fqng denote an ordering of all rational numbers in 0; 1. (a) For the ordering...

5. Let fqng denote an ordering of all rational numbers in ½0; 1.

(a) For the ordering implied by Cantor’s construction in section 2.1.4, including or excluding multiple counts, demonstrate that for every n, Un ¼ 1, Ln ¼ 0, and hence lim sup qm ¼ 1 and lim inf qm ¼ 0.

(b) Generalize the result on part

(a) by showing that the same conclusion follows for an arbitrary ordering.