Set Equivalence/Examples/Arbitrary Example 1
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Example of Set Equivalence
Let:
| \(\ds S\) | \(=\) | \(\ds \set {2, 4, 6, 8}\) | ||||||||||||
| \(\ds T\) | \(=\) | \(\ds \set {3, 5, 7, 9}\) |
There exists a bijection between $S$ and $T$, that is: $f : x \mapsto x + 1$, for example.
They both have the same cardinality, that is $4$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): one-to-one correspondence ($\text {1-1}$ correspondence)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): one-to-one correspondence (one-one or $\text {1-1}$ correspondence)