irrational vs illogical

irrational is a noun but illogical is not a noun.

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

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

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