1. Let S be a subset of . Prove that S is compact iff every infinite subset of S has an accumulation point in S. 2. In any ordered field F, we can define absolute value in the usual way: | x | = x if...

1. Let S be a subset of
. Prove that S is compact iff every infinite subset of S has an accumulation point in S.

2. In any ordered field F, we can define absolute value in the usual way: | x | = x if x ≥ 0 and | x | = – x if x <>

(a) Let F be the ordered field of rational numbers
.

(b) Let F be the ordered field of rational functions F.