Elements of Set
Elements are the objects contained in a set. A set may be defined by a common property amongst the objects.
The mathematical notation for "is an element of" is \inβ. For example, to denote that 22 is an element of the set EE of positive even integers, one writes 2 \in E2βE.
Let us take an example:
A = {1, 2, 3, 4, 5 }
Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated.
All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 β A, 2 β A etc. The cardinal number of the set is 5.
Some commonly used sets are as follows:
N: Set of all natural numbers
Z: Set of all integers
Q: Set of all rational numbers
R: Set of all real numbers
Z+: Set of all positive integers
Order of sets
The order of a set defines the number of elements a set is having. It describes the size of a set. The order of set is also known as the cardinality.
The size of set whether it is is a finite set or an infinite set said to be set of finite order or infinite order, respectively.