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Could somebody throw their hat in with me on these?

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

Limit point = 1 , Isolated points are equal to the whole set

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

Limit points are -1 and 1, Isolated points are the whole set

c. [tex](0,1) \cup 2[/tex]

Limit points are [0,1], Isolated point is 2.

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

Limit points none, Isolated points are [tex]\mathbb{N}[/tex]

e. [tex] \mathbb{R} \backslash \mathbb{Q}[/tex]

Limit points are [tex]\mathbb{R}[/tex], Isolated points are none.

f. [tex] \mathbb{Q} \cap (0,1) [/tex]

Limits points are [0,1], Isolated points are none

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

Limit point = 1 , Isolated points are equal to the whole set

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

Limit points are -1 and 1, Isolated points are the whole set

c. [tex](0,1) \cup 2[/tex]

Limit points are [0,1], Isolated point is 2.

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

Limit points none, Isolated points are [tex]\mathbb{N}[/tex]

e. [tex] \mathbb{R} \backslash \mathbb{Q}[/tex]

Limit points are [tex]\mathbb{R}[/tex], Isolated points are none.

f. [tex] \mathbb{Q} \cap (0,1) [/tex]

Limits points are [0,1], Isolated points are none

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