 # GMAT Quant: Arithmetic – Numbers What are Numbers?

Technically, we have known 1, 2, 3…… etc. as the numbers but we never actually knew  much on its definition.

A number is a mathematical object that is used for calculating, counting or labeling.

Numbers can be divided into many categories and a particular number can belong to many categories at the same time. Let’s refresh the main categories of arithmetic numbers.

• Natural numbers (N): The counting numbers starting from 1 up to infinity are known as natural numbers.
• Whole Numbers (W): Natural numbers together with 0 forms the category of whole numbers.
• Integers (Z): All positive and negative numbers forms this category. {……-2, -1, 0, 1, 2……}
• Real Numbers (R): These numbers have decimal representations with a finite or infinite sequence of numbers to the right of the decimal point. It can be zero, positive or negative.
• Rational numbers (Q): Numbers that can be expressed in the form of a ratio of integer versus non-zero integer denominator. It can be zero, positive or negative. All rational numbers are real but the converse is not true.
• Irrational Numbers (I): The set of numbers left after removing rational numbers from real numbers. An irrational number cannot be expressed in form of p/q. Non-recurring decimal numbers are also known as irrational number.
• Imaginary Number: After multiplying real numbers with square root of -1, the value we get is known as imaginary numbers.
• Complex Number (C): Sum or difference of real and imaginary numbers makes complex numbers.
• Hypercomplex numbers: It includes various extensions of number systems, such as, biquaternions., coquaternions, sedenions, tessarines, octonions, and quaternions.

These are the basic concepts and categories of arithmetic numbers. There is nothing new in these definitions and you have learnt them in your primary school. Just read them once and all the concepts will be refreshed.

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Read more on Integers and Percentages.