Wiktionary
n. (context mathematics English) Any real number that cannot be expressed as a ratio of two integers.
WordNet
n. a real number that cannot be expressed as a rational number
Wikipedia
In mathematics, an irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction. Therefore, irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat. For example, the number starts with 3.14159265359, but no finite number of digits can represent it exactly and it does not end in a segment that repeats itself infinitely often. The same can be said for any irrational number.
As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.
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.
Numbers which are irrational include the ratio of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two; in fact all square roots of natural numbers, other than of perfect squares, are irrational.
Usage examples of "irrational number".
They showed tow-to-the power-of-Infinity-minus-one (an irrational number that only has a conventional meaning in Improbability physics).
Pi's what they call an irrational number, three and an infinitely long string of numbers after the decimal point.
They showed tow-to-the power- of-Infinity-minus-one (an irrational number that only has a conventional meaning in Improbability physics).
And so, in that Greek letter that looks like a shack with a corrugated tin roof, in that elusive, irrational number with which scientists try to understand the universe, I found refuge.