Prove supS ≤ infT - Math Homework

[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?