# Prove supS <= infT

## Homework Statement

Let S and T be non-empty subsets of R, and suppose that for all s $$\in$$ S and t $$\in$$ T, we have s $$\leq$$ t.

Prove that supS $$\leq$$ infT.

N/A

## The Attempt at a Solution

Since s $$\in$$ S $$\Rightarrow$$ s $$\in$$ T, supT is an upper bound for S.
Since supS is the least upper bound, supS $$\leq$$ supT.

How does this look to you? Feedback is appreciated.

$$supS \leq supT$$ doesn't seem that useful as a start to be honest (supT and infT aren't very close to each other in general). To show that $$supS \leq infT$$, can you show that infT is an upper bound of S?