# Subset

set whose elements are all contained in another set

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}.
${\displaystyle [0,1]\subset \mathbb {R} }$
${\displaystyle [0,1]\subset \mathbb {R} _{+}}$
• {46,189,1264} is its own subset, and is a proper subset of the set of natural numbers.
${\displaystyle \{46,189,1264\}\subseteq \{46,189,1264\}}$
${\displaystyle \{46,189,1264\}\subset \mathbb {N} }$

## References

1. "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-08-23.
2. Weisstein, Eric W. "Subset". mathworld.wolfram.com. Retrieved 2020-08-23.
3. "Introduction to Sets". www.mathsisfun.com. Retrieved 2020-08-23.