volume_mute
N is Equivalent to M = {1/n | n ∈ N}
publish date: 2026/05/23 21:45:32.847299 UTC
volume_mute
The table below pairs each natural number \(n\) with the fraction \(1/n\).
| Participation Type | Description | Minimum Cardinality |
|---|---|---|
| Total Participation | Every entity in the set must be involved in at least one relationship. | 1 |
| Partial Participation | Entities in the set may or may not be involved in a relationship. | 0 |
What can be concluded from this pairing?
Correct Answer
N and M are equivalent sets — they have the same cardinality
Explanation
The function \(f(n) = 1/n\) defines a bijection from \(\mathbb{N}\) to \(M = \{1/n \mid n \in \mathbb{N}\}\). Each natural number \(n\) is paired with exactly one fraction \(1/n\), and every element of \(M\) has exactly one pre-image. So \(N \sim M\) — they are equivalent. They are not equal since, for instance, \(2 \in N\) but \(2 \notin M\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012