Number is one the the basic concepts of mathematics. It is probably the very first idea we learn as a child. Here I want to present various numbers in use.

  1. Natural numbers: Natural numbers are unending consecutive numbers starting from 1. Example 1, 2, 3, ..., ..., 11, 12, 13, ... 111, 112, 113, ..., ..., ... . Set of natural number is denoted by N = { 1, 2, 3, ..., ..., ... }
  2. Integers: Integers are set of natural numbers together with their negatives and also includes zero. The set of integers is denoted by I. I = { ...., -3, -2, -1, 0, 1, 2, 3, .... }
  3. Rational numbers: A rational number is a number which can be expressed as a ratio of two integers. Rational number is expressed in the form \frac{p}{q} where p and q are integers and q \neq 0 . A rational number can also be expressed as terminating decimal or as a repeating decimals. Some examples of rational numbers are 2, -5, -\frac{1}{3}, \frac{4}{3}, 0.2345 . A set of rational number is mathematically denoted by Q. Q = { x : x = \frac{p}{q}, p\ and\ q\ are\ integers\ and\ q\ \neq 0 }
  4. Irrational numbers: Numbers which are not rational are irrational. So any number which cannot be expressed as the ratio of two integers is known as irrational number. Some examples \sqrt{5}, \sqrt[3]{7}

Real Number system

The set of all rational and irrational numbers taken together form a new system of numbers known as real number system. One important property of the real numbers is that they are ordered. This is between tow real numbers p and q, only one relation p = q,\ p > q\ or\ p < q holds.