Example · High school
Terms
| Term | This example | Why |
|---|
| union |
$A \cup B = \setdef{\text{apple}, \text{orange}, \text{banana}}$
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| intersection |
$A \cap B = \setdef{\text{orange}}$
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| disjoint union (of disjoint sets) |
None
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The union of $A = \setdef{\text{apple}, \text{orange}}$ and $B = \setdef{\text{orange}, \text{banana}}$ is not a union of disjoint sets, because $A$ and $B$ overlap.
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| disjoint union (tagged) |
$A \sqcup B = \setdef{(1, \text{apple}), (1, \text{orange}), (2, \text{orange}), (2, \text{banana})}$
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The tagged disjoint union keeps both copies of orange, so it has $4$ elements.
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Distinctions using this example
- Disjoint union: union of disjoint sets vs. tagged union: $A$ and $B$ overlap, so their ordinary union $\setdef{\text{apple}, \text{orange}, \text{banana}}$ is not a disjoint union in either sense. The tagged disjoint union keeps both copies of orange, so it has $4$ elements.
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