First Proof That Two Sets Are Equal

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Problem 8: (First Proof That Two Sets Are Equal)

Let $I=(5,9] $. Consider the sets $S=\{x\mid x \text{ is an upper bound of } I\}$ and $A=\{x\mid x\geq 9\} $. Prove that $S=A$.

• Start by proving that $S\subseteq A$. So show that every element of $S$ is an element of $A$.
• Then prove that $A\subseteq S$.

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