Tuesday, 14 May 2013

Number System | Binary | Hexadecimal | Roman | Fractions

Types of Numbers

Natural numbers (ℕ)

The counting numbers {1, 2, 3, ...}, are called natural numbers. They include all the counting numbers i.e. from 1 to infinity.

Whole numbers (w)

They are the natural numbers including zero. Not all whole numbers are natural numbers, but all natural numbers are whole numbers.

Integers (Z)

Positive and negative counting numbers, as well as zero.

Rational numbers (Q)

Numbers that can be expressed as a fraction of an integer and a non-zero integer.

Real numbers (ℝ)

All numbers that can be expressed as the limit of a sequence of rational numbers. Every real number corresponds to a point on the number line.

Irrational numbers

A real number that is not rational is called irrational.

Complex Numbers (C)

Includes real numbers and imaginary numbers, such as the square root of negative one.

Hypercomplex numbers (C)

Includes various number-system extensions: quaternions, octonions, tessarines, coquaternions, and biquaternions.


Number representations

Decimal
The standard Hindu–Arabic numeral system using base ten.

Binary
The base-two numeral system used by computers.

Roman
The numeral system of ancient Rome, still occasionally used today.

Fractions
A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers.

Scientific Notation
A method for writing very small and very large numbers using powers of 10. When used in science, such a number also conveys the precision of measurement using significant figures.

Knuth's up-arrow notation and Conway chained arrow notation
Notations that allow the concise representation of extremely large integers such as Graham's number.

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