irrational vs unlogical

irrational is a noun but unlogical is not a noun.

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

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

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