The Integers Have No Limit Points

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Problem 31: (The Integers Have No Limit Points)

There are three parts to this problem.

• Start by writing the definition of a limit point $p$ of a set $S$ using the quantifiers $\forall$ and $\exists$. Feel free to use set operations $\cup$ and/or $\cap$ in your definitions.
• Then write, using these quantifiers, what it means to not be a limit point.
• Finish by proving that if $p\in\mathbb{R}$, then $p$ is not a limit point of $\mathbb{Z}$. In other words, prove that $\mathbb{Z}$ has no limit points.

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