Sets and their Notation

Sets

A set is a collection of well defined objects. The objects of a set are taken as distinct only on the ground of simplicity.Each element in a set is unique.

Notation: Usually a set is denoted by a capital letter e.g., A, B, ....., U, V etc. and the elements are
enclosed within brackets { }, denoted by small letters a, b, ....., x, y etc.
For example:
                                                  A = Set of all small English alphabets
                                                      = {a, b, c, ....., x, y, z}
                                                   R = Set of real numbers
                                                      = {x: -∞ < x < ∞}

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

A set of sets is frequently called a family or collection of sets.

For example, suppose we have a family of sets consisting A1, A2, A3,….. up to An, that is the family {A1, A2, A3,….., An } and could be denoted as

S = {Ai | i belongs to N and 1 ≤ i ≤ n}

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