Subset

A subset is a set which has some (or all) of the elements of another set, called 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.

Examples:

• {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 or the set of positive numbers.

[math]\displaystyle{ [0;1] \subset R }[/math]

[math]\displaystyle{ [0;1] \subset (R~\backslash ~R_-) }[/math]

• {46,189,1264} is its own subset, and it's a proper subset of the set of natural numbers.

[math]\displaystyle{ \{ 46,189,1264\} \subseteq \{ 46,189,1264\} }[/math]

[math]\displaystyle{ \{ 46,189,1264\} \subset N }[/math]