$A = \lbrace \text{apple} \rbrace$ and $B = \lbrace \text{banana} \rbrace$
Terms
| Term | This example | Why |
|---|---|---|
| union | $A \cup B = \lbrace \text{apple}, \text{banana} \rbrace$ | |
| disjoint union (of disjoint sets) | $A \cup B = \lbrace \text{apple}, \text{banana} \rbrace$ | |
| disjoint union (tagged) | $A \sqcup B = \lbrace (1, \text{apple}), (2, \text{banana}) \rbrace$ | Each element is tagged with $1$ (from $A$) or $2$ (from $B$). The result is usually identified with $\lbrace \text{apple}, \text{banana} \rbrace$. |
Distinctions using this example
- Disjoint union: union of disjoint sets vs. tagged union: $A$ and $B$ are disjoint, so their union is a union of disjoint sets. The tagged disjoint union is usually identified with it.