The difference between Illogical and Irrational
When used as adjectives, illogical means contrary to logic, whereas irrational means not rational.
Irrational is also noun with the meaning: a real number that can not be expressed as the quotient of two integers, an irrational number.
check bellow for the other definitions of Illogical and Irrational
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Illogical as an adjective:
Contrary to logic; lacking sense or sound reasoning.
Examples:
"I received an illogical reply and that left me standing there feeling confused."
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Irrational as an adjective:
Not rational; unfounded or nonsensical.
Examples:
"an irrational decision"
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Irrational as an adjective (mathematics, arithmetic, number theory, not comparable):
Of a real number, that cannot be written as the ratio of two integers.
Examples:
"The number π is irrational."
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Irrational as a noun:
A real number that can not be expressed as the quotient of two integers, an irrational number.