Question

Show that,given any element x of the set (0,infinity) ,there is another element y in (0,infinity) with the property that y < x . Deduce that (0,infinity) has no minimum.

Answer 1

let y = x/2

then for all x in (0, inf)
x/2 < x
x < 2x
1 < 2 (true)

(0,inf) has no minimum because no matter what x is, there is always another element in (0,inf) that is less than x. Namely x/2

Answer 2

oh okay..thank you very much :)