consider the set S = {n+(1/m): m,n in N}. show that N subset of S'.

To show that \( \mathbb{N} \subseteq S' \) (where \( S' \) is the complement of the set \( S \), meaning the set of limit points of \( S \)), we need to:

1. **Understand the set \( S \)**:  
   The set \( S \) consists of elements of the form \( n + \frac{1}{m} \), where \( n \in \mathbb{N} \) (the natural numbers) and \( m \in \mathbb{N} \). In other words, for any natural numbers \( m \) and \( n \), \( S \) contains elements like:
   \[
   S = \left\{ n + \frac{1}{m} \mid n, m \in \mathbb{N} \right\}
   \]

   These are numbers that are slightly larger than natural numbers because of the term \( \frac{1}{m

Consider the set S = {n+(1/m): m,n in N}. Show that N subset of S'.

Explore the proof showing that the set of natural numbers is a subset of the limit points of the set S = {n + (1/m) | n, m ∈ N}. This problem involves concepts from set theory, real analysis, and limit points. Ideal for students at the undergraduate level.

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