1 . Let S={n N: n= 2^mfor some m N}.

. Prove that S has no maximum.

. Determine what is min S

2. Let us extend the previous exercises a bit more. Let f:RR be a strictly decreasing

function. Prove that the set{f(1), f(2), f(3), . . .} does not contain a minimum

3. Let S denote the set of rational numbers q such that

q<3

in lowest terms, the denominator of q is a power of two.

Prove that S does not have a maximum