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fiddling with math some more
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hanjoosten committed Dec 2, 2024
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Expand Up @@ -86,17 +86,17 @@ When coding in Ampersand, these operators are typed with characters on the keybo

:::info Note on `hashtag`

`hashtag` used to be pronounced as `cartesian product`. However, this is an incorrect term for this operator. The Cartesian product of two terms \( R \) and \( S \) is defined as the set of all pairs where the first element is a pair from \( R \) and the second element is a pair from \( S \). Mathematically:
`hashtag` used to be pronounced as `cartesian product`. However, this is an incorrect term for this operator. The Cartesian product of two terms $$R$$ and $$S$$ is defined as the set of all pairs where the first element is a pair from \( R \) and the second element is a pair from \( S \). Mathematically:

$$
R \times S = \{ ((a, b), (c, d)) \mid (a, b) \in R \text{ and } (c, d) \in S \}.
$$

***Explanation***:
1. **Relation $ R $:** A subset of the Cartesian product of two sets $ A $ and $ B $, i.e., $ R \subseteq A \times B $.
2. **Relation $ S $:** A subset of the Cartesian product of two sets $$ C $$ and $$ D $$, i.e., $$ S \subseteq C \times D $$.
2. **Relation $ S $:** A subset of the Cartesian product of two sets $$C$$ and $$D$$, i.e., $$S \subseteq C \times D$$.

The Cartesian product $$ R \times S $$ forms a new term in which each element is a pair of pairs: one pair from $$ R $$ and another pair from $$ S $$.
The Cartesian product $$ R \times S $$ forms a new term in which each element is a pair of pairs: one pair from $$R$$ and another pair from $$S$$.

***Example***:
Let $$ R = \{(1, 2), (3, 4)\} $$ and $$ S = \{(5, 6), (7, 8)\} $$. Then:
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