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Subset

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We say a set A is a subset of another set B if every element of A is also an element of B, and we denote this by A \sub B. The empty set is a subset of every set, and every set is a subset of itself. The notation A \subseteq B emphasizes that A may be equal to B, while A \subsetneq B says that A is any subset of B other than B itself.


The following is a true statement:

\emptyset \sub \{1, 2\} \sub \mathbb{N} \sub \mathbb{Z} \sub \mathbb{Q} \sub \mathbb{R} \sub \mathbb{C} \sub \mathbb{C}\, \cu...


The set of all subsets of a given set S is called the power set of S and is denoted \mathcal{P}(S) or 2^S.

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