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Irrational
Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. The term is used, usually pejoratively, to describe thinking and actions that are, or appear to be, less useful, or more illogical than other more rational alternatives.Irrational behaviors of individuals include taking offense or becoming angry about a situation that has not yet occurred, expressing emotions exaggeratedly (such as crying hysterically), maintaining unrealistic expectations, engaging in irresponsible conduct such as problem intoxication, disorganization, and falling victim to confidence tricks. People with a mental illness like schizophrenia may exhibit irrational paranoia.
These more contemporary normative conceptions of what constitutes a manifestation of irrationality are difficult to demonstrate empirically because it is not clear by whose standards we are to judge the behavior rational or irrational.
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Irrational (adjective)
Not rational; unfounded or nonsensical.
“an irrational decision”
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Irrational (adjective)
Of a real number, that cannot be written as the ratio of two integers.
“The number π is irrational.”
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Irrational (noun)
A real number that can not be expressed as the quotient of two integers, an irrational number.
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Arational (adjective)
Not within the domain of what can be understood or analyzed by reason; not rational, outside the competence of the rules of reason. from 20th c.