Question: 1. Let S, T be non-empty, bounded sets. Let the set U={u R:u=st, s S, t T}.Prove that supU=sup SinfT. 2 Consider the list of

1.

Let S, T be non-empty, bounded sets. Let the set U={u R:u=st, s S, t T}.Prove that supU=sup SinfT.

2

Consider the list of intervals[a1, b1],[a2, b2],[a3, b3], . . . . Assume that for any i, j N, ai<

bj.

Prove that the intersection of all the intervals in this list is non-empty (i.e., prove that there is

some x that belongs to all the intervals).

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