Integer vs. Irrational — What's the Difference?

An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Not endowed with reason.

A number which is not a fraction; a whole number

Affected by loss of usual or normal mental clarity; incoherent, as from shock.

A thing complete in itself.

Marked by a lack of accord with reason or sound judgment

A member of the set of positive whole numbers {1, 2, 3, ... }, negative whole numbers {-1, -2, -3, ... }, and zero {0}.

Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.

A complete unit or entity.

Being a metric foot containing such a syllable.

(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

(Mathematics) Of or relating to an irrational number.

A complete entity; a whole number, in contradistinction to a fraction or a mixed number.

An irrational number.

Any of the natural numbers (positive or negative) or zero

Not rational; unfounded or nonsensical.

Of a real number, that cannot be written as the ratio of two integers.

A real number that can not be expressed as the quotient of two integers, an irrational number.

Not rational; void of reason or understanding; as, brutes are irrational animals.

Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; - of assertions and beliefs.

Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; - said especially of roots. See Surd.

Not consistent with or using reason;

Real but not expressible as the quotient of two integers;