Irrational number

In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a ratio of two integers, i.e., it is not of the form

Related Topics:
Mathematics - Real number - Rational number - Integer

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:a/b

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

where a and b are integers and b is not zero. It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc) never ends and never enters a periodic pattern, but no mathematician takes that to be a definition. Almost all real numbers are irrational, in a sense which is defined more precisely below.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Some irrational numbers are algebraic numbers, such as √2, the square root of two, and 3√5, the cube root of 5; others are transcendental numbers such as π and e.

Related Topics:
Algebraic number - Square root - Two - Cube root - Transcendental number - π - E

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common. A measure of a line segment I in this sense is a line segment J that "measures" I in the sense that some whole number of copies of J laid end-to-end occupy the same length as I.

Related Topics:
Ratio - Incommensurable

~ ~ ~ ~ ~ ~ ~ ~ ~ ~