# 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 A_{1}, A_{2}, A_{3},….. up to A_{n}, that is the family {A_{1}, A_{2}, A_{3},….., A_{n} } and could be denoted as

S = {A_{i} | 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**.