- #1

The Captain

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## Homework Statement

Given A and B are sets of numbers, [tex]A \neq \left\{ \right\} [/tex], [tex]B[/tex] is bounded above, and [tex] A \subseteq B [/tex].

Explain why sup(A) and sup(B) exist and why [tex]sup(A) \leq sup(B)[/tex].

## Homework Equations

[tex] \exists r \in \mathbb R \: : \: r \geq a \: \forall a \in A [/tex]

[tex] \exists r \in \mathbb R \: : \: A \subset \left[ - \infty , r \right] [/tex]

## The Attempt at a Solution

If [tex] k \in B: k \geq s, \: \forall s \in S [/tex]. Then [tex] k = sup(B)[/tex].

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