If X and Y are sets and every element of X is also an element of Y, then we say or write:
Every set Y is a subset of itself. A subset of Y which is not equal to Y is called proper. If X is a proper subset of Y, then we write X ⊂ Y. Analogous comments apply to supersets.
There are two major systems in use for the notation of subsets. The older system uses the symbol "⊂" to indicate any subset and uses "⊊" to indicate proper subsets. The newer system uses the symbol "⊆" to indicate any subsets and uses "⊂" to indicate proper subsets. Wikipedia uses the newer system, which can be handled by a wider variety of web browsers. Analogous comments apply to supersets.
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