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Classification of Numbers

This classification of Numbers represents the most accepted elementary classification, and is useful in computing sense.

Classification of Numbers

ClassSymbolDescription
Natural NumberNatural Number SymbolNatural numbers are defined as non-negative counting numbers: Natural Number Symbol = { 0, 1, 2, 3, 4, ... }. Some exclude 0 (zero) from the set: Natural Number Symbol* = Natural Number Symbol\{0} = { 1, 2, 3, 4, ... }.
IntegerInteger SymbolIntegers extend Natural Number Symbol by including the negative of counting numbers:
Integer Symbol = { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }.
The symbol Integer Symbol stands for Zahlen, the German word for "numbers".
Rational NumberRational Number SymbolA rational number is the ratio or quotient of an integer and another non-zero integer:
Rational Number Symbol = {n/m | n, m ∈ Integer Symbol, m ≠ 0 }.
E.g.: -100, -20¼, -1.5, 0, 1, 1.5, 1½ 2¾, 1.75, &c
Irrational NumberIrrational numbers are numbers which cannot be represented as fractions.
E.g.: √2, √3;, π, e.
Real NumberReal Number SymbolReal numbers are all numbers on a number line. The set of Real Number Symbol is the union of all rational numbers and all irrational numbers.
Imaginary NumberAn imaginary number is a number which square is a negative real number, and is denoted by the symbol i, so that i2 = -1.
E.g.: -5i, 3i, 7.5i, &c.
In some technical applications, j is used as the symbol for imaginary number instead of i.
Complex NumberComplex Number SymbolA complex number consists of two part, real number and imaginary number, and is also expressed in the form a + bi (i is notation for imaginary part of the number).
E.g.: 7 + 2i


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