- #1

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## Homework Statement

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition).

I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...

I need help with a part of Exercise 2.2.4 Part (3) ... ...

Exercise 2.2.4 Part (3) reads as follows:

## Homework Equations

The definitions of open and closed sets are relevant as is the definition of an \epsilon neighborhood. Sohrab defines these concepts/entities as follows:

## The Attempt at a Solution

Reflecting in general terms, I suspect the proof that ##\mathbb{N}## and ##\mathbb{Z}## are closed is approached by looking at the complements of the sets of ##\mathbb{N}## and ##\mathbb{Z}## ... visually ##\mathbb{R}## \ ##\mathbb{N}## and ##\mathbb{R}## \ ##\mathbb{Z}## and proving that these sets are open ... which intuitively they seem to be ... but I cannot see how to technically write the proof in terms of open sets and ##\epsilon##-neighbourhoods ... can someone please help ...

I have not made any progress regarding the set ##\{ \frac{1}{n} \ : \ n \in \mathbb{N} \}## ...

Peter