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N is Equivalent to the Set of Even Natural Numbers
publish date: 2026/05/23 21:45:33.115038 UTC
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The table shows a correspondence between all natural numbers and all even natural numbers.
| Term | Definition | Example |
|---|---|---|
| Cardinality | The total number of rows (tuples) in the relation. | 500 |
| Degree | The total number of columns (attributes) in the relation. | 50 |
The function used is \(f(x) = 2x\). What does this demonstrate?
Correct Answer
The even numbers form an equivalent set to all natural numbers — they have the same cardinality
Explanation
\(f(x) = 2x\) is a bijection from \(\mathbb{N}\) to the even numbers \(M = \{2,4,6,8,\ldots\}\). Even though \(M \subsetneq \mathbb{N}\) (M is a proper subset of N), the bijection shows \(N \sim M\). This is a hallmark of infinite sets: an infinite set can be equivalent to one of its own proper subsets. We may say: there are as many even numbers as there are natural numbers.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012