ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D70
Set difference

Let $X$ and $Y$ each be a D11: Set.
The difference of $X$ and $Y$ is the D11: Set $$X \setminus Y : = \{ x \in X : x \not\in Y \}$$

Let $X$ and $Y$ each be a D11: Set.
The difference of $X$ and $Y$ is the D11: Set $$X \setminus Y : = \{ x : x \in X \text{ and } x \not\in Y \}$$
Children
 ▶ Set complement ▶ Symmetric set difference
Results
 ▶ Antitonicity of subtracting from the same set ▶ Difference of set and binary union equals intersection of differences ▶ Difference of set and countable union equals intersection of differences ▶ Difference of set and finite union equals intersection of differences ▶ Isotonicity of subtracting same set ▶ Set difference equals intersection with complement ▶ Set difference is subset of the minuend
Conventions
 ▶ Convention 0 (Notation for set difference) If $X$ and $Y$ are each a D11: Set, we denote the D70: Set difference of $X$ and $Y$ by $X \setminus Y$.