Set Equivalence/Examples/Arbitrary Example 2
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Example of Set Equivalence
Let:
| \(\ds A\) | \(=\) | \(\ds \set {1, 2, 3}\) | ||||||||||||
| \(\ds B\) | \(=\) | \(\ds \set {1, 2, 3, 4, 5}\) |
There does not exists a bijection between $A$ and $B$.
That is because they do not have the same cardinality.
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)