# Subset

A set $$S_0$$ is a subset of a set $$S_1$$ if every element of $$S_0$$ is an element of $$S_1$$, but not necessarily vice versa.
For example, the set $$A = \{1, 2, 3\}$$ is a subset of both $$B = \{1, 2, 3\}$$ and $$C = \{1, 2, 3, 4\}$$.
If $$S_1$$ definitely has elements not in $$S_0$$ we write $$S_0 \subset S_1$$, otherwise we write $$S_0 \subseteq S_1$$, much as we do for inequalities with $$x_0 < x_1$$ and $$x_0 \leqslant x_1$$.
In the first case, $$S_0$$ is known as a proper subset of $$S_1$$.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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