- #1
The_Iceflash
- 50
- 0
Homework Statement
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.
Homework Equations
N/A
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.
How does this look to you? Feedback is appreciated.