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## 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 sup

*S*[tex]\leq[/tex] inf

*T*.

## Homework Equations

N/A

## The Attempt at a Solution

Since

*s*[tex]\in[/tex]

*S*[tex]\Rightarrow[/tex]

*s*[tex]\in[/tex]

*T*, sup

*T*is an upper bound for

*S*.

Since sup

*S*is the least upper bound, sup

*S*[tex]\leq[/tex] sup

*T*.

How does this look to you? Feedback is appreciated.