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## Homework Statement

Let S and T be nonempty subsets of [tex]\mathbb{R} \backepsilon s \leq t \forall s \in S \wedge t \in T.[/tex] A) Observe that S is bounded above and that T is bounded below. B) Prove that [tex]sup S = inf T.[/tex]

## Homework Equations

## The Attempt at a Solution

Let [tex] s_0 = sup S. \text{ Then } s \leq s_o \forall s \in S \wedge s \leq t \forall s \in S \Rightarrow s_0 \leq t. [/tex]

Let [tex] t_0 = inf S. \text{ Then } t_0 \leq t \forall t \in T \wedge s \leq t \forall t \in T \Rightarrow s \leq t_0. [/tex]