illogical vs irrational

illogical is not a noun while irrational is a noun.

Word	Noun	Adjective	Verb	Adverb
illogical	No	Yes	No	No
irrational	Yes	Yes	No	No

illogical (noun)	irrational (noun)
	a real number that cannot be expressed as a rational number

illogical (adjective)	irrational (adjective)
lacking in correct logical relation	not consistent with or using reason
lacking orderly continuity	real but not expressible as the quotient of two integers