# Math Help - Proving that sup S \leq inf T

1. ## Proving that sup S \leq inf T

Given the following, I need to show that $sup S \leq inf T.$ Let S and T be nonempty subsets of $\mathbb{R} \backepsilon s \leq t \forall s \in S \wedge t \in t.$
A) Observe that S is bounded above and that T is bounded below.
B) Prove that $sup S \leq inf T.$
C) Given an example of such sets S and T where $S \cap T \neq \varnothing.$

2. (b) follows immediately from the definitions of sup and inf.

(c) Let $S=[0,1/2]$ and $T=[1/2,1]$.