Homework Help: Prove supS <= infT

1. The problem statement, all variables and given/known data
Let S and T be non-empty subsets of R, and suppose that for all s [tex]\in[/tex] S and t [tex]\in[/tex] T, we have s [tex]\leq[/tex] t.

Prove that supS [tex]\leq[/tex] infT.

2. Relevant equations
N/A


3. The attempt at a solution

Since s [tex]\in[/tex] S [tex]\Rightarrow[/tex] s [tex]\in[/tex] T, supT is an upper bound for S.
Since supS is the least upper bound, supS [tex]\leq[/tex] supT.


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