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a.) Construct a subset of [tex]\mathbb{R}[/tex] with exactly two limit points.

[tex]\{ (-1)^n + \frac{1}{n} : n \in \mathbb{N} \} [/tex]

b.) Find an infinite subset of [tex]\mathbb{R}[/tex] with no limit points.

[tex]\mathbb{N}[/tex]

c.) Construct a countable subset of [tex]\mathbb{R}[/tex] with countably many limit points.

[tex]\{1- \frac{(-1)^n}{n}:n \in \mathbb{N} \}[/tex]

d.) Find a countable subset of [tex]\mathbb{R}[/tex] with uncountably many limit points.

[tex]\mathbb{Q}[/tex]

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# Homework Help: More Limit pts sets

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