Set and subset

A set is collection of different mathematical objects called elements, which can be numbers, people, colours, matrices, etc. Examples of sets are {4, 20, 83, 1059, …} and {red, blue, cyan, grey}, where the former is an infinite set and the latter is a finite set. Two sets $A$ and $B$ are equal if they have the same elements, e.g. $A=\{3,10,17\}$ and $B=\{17,3,10\}$ . A set with no element, denoted by $\varnothing$ , is called an empty set. An element $k$ in a set $A$ is denoted by $k\in A$ .

A subset is an equal or smaller collection of elements of a particular set. With reference to the above diagram, the set $A=\{7,13,58\}$ is a subset of the set $B=\{1,5,7,13,58,82,296,941\}$ , which is mathematically denoted by $A\subseteq B$ . Similarly, $\varnothing\subseteq B$ and $B\subseteq B$ .