Subset
set whose elements are all contained in another set From Wikipedia, the free encyclopedia
In set theory, a subset is a set which has some (or all) of the elements of another set, called a superset, but does not have any elements that the superset does not have. A subset which does not have all the elements of its superset is called a proper subset. We use the symbol ⊆ to say a set is a subset of another set. We can also use ⊂ if it is a proper subset. The symbols ⊃ ⊇ are opposite - they tell us the second element is a (proper) subset of the first.[1][2][3]
For example:
- {1, 2, 3} is a proper subset of {-563, 1, 2, 3, 68}.
- The interval [0, 1] is a proper subset of the set of real numbers (also the set of positive numbers).
![{\displaystyle [0,1]\subset \mathbb {R} }](http://wikimedia.org/api/rest_v1/media/math/render/svg/98ef6fb8c5d9b34f4ba677930a956bd62270f9a2)
![{\displaystyle [0,1]\subset \mathbb {R} _{+}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/43dbf4ecb8ec65141f7e3e20f13800c1457c1fde)
- {46,189,1264} is its own subset, and is a proper subset of the set of natural numbers.
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