Prove supS <= infT

[The_Iceflash]

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.

Homework Equations

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.

 

[Office_Shredder]

$$supS \leq supT$$ 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?