Difference between Illogical and Irrational

ILLOGICAL vs IRRATIONAL: NOUN

A prime number.
In mathematics, an irrational number, that is, the mark of a cut which separates all rational numbers into two classes, the first having no greatest number, the second no least.
That which is devoid of reason, as one of the lower animals.
A real number that can not be expressed as the quotient of two integers, an irrational number.
An irrational number.

Marked by a lack of accord with reason or sound judgment.
Affected by loss of usual or normal mental clarity; incoherent, as from shock.
Not endowed with reason.
Real but not expressible as the quotient of two integers
Not consistent with or using reason
Being a metric foot containing such a syllable.
Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
Of or relating to an irrational number.
Not rational; void of reason or understanding.
Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs.
Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; -- said especially of roots. See Surd.
Not rational; unfounded or nonsensical.
Of a real number, that cannot be written as the ratio of two integers.

Ignorant or negligent of the rules of logic or sound reasoning: as, an illogical disputant.
Contrary to the rules of logic or sound reasoning: as, an illogical inference.
Synonyms Inconclusive, inconsequent, unsound, fallacious, sophistical.

Not rational; without the faculty of reason; void of understanding; unreasoning.
Without the quality of reason; contrary to reason; illogical; unreasonable: as, irrational motives; an irrational project.
In mathematics: In arithmetic, not capable of being exactly expressed by a vulgar fraction, proper or improper; surd.
In translations of Euclid, and cognate writings, at once incommensurable with the assumed unit and not having its square commensurable with that of the unit. This is the peculiar meaning given by Euclid to α%27λογος, though Plato uses it in sense , above.
In algebra, noting a quantity involving a variable raised to a fractional power; or. in a wider sense, noting a quantity not rational, not a sum of products of constants and of variables into one another or into themselves.
In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.

Unlogical, Scattered, Disconnected, Intuitive, Garbled, Disordered, Unconnected, Disjointed, Confused, Inconsequential, Incongruous, Nonrational, Incoherent, Unreasonable, Absurd

Unjustified, Irresponsible, Perverse, Insane, Rational, Illogical, Reasonless, Yellow, Blind, Jaundiced, Superstitious, Incoherent, Unreasoning, Unreasonable, Nonrational

Unlogical, Scattered, Disconnected, Intuitive, Garbled, Disordered, Unconnected, Disjointed, Confused, Inconsequential, Incongruous, Nonrational, Incoherent, Unreasonable, Absurd

Unjustified, Irresponsible, Perverse, Insane, Rational, Illogical, Reasonless, Yellow, Blind, Jaundiced, Superstitious, Incoherent, Unreasoning, Unreasonable, Nonrational

The existing situation is both unfair and illogical.
It would be illogical to do anything else.
If this sounds illogical and convoluted, it is.
And, then there was the horrible illogical writing.
It is illogical to separate these two processes.
Like the period in illogical places, we notice.
Completely unscientific and illogical, what was the harm.
Then again, so are people, illogical that is.
Attorney general Mahbubey Alam termed the demand illogical.
If a human being can be such a thing is not illogical, why is the hypostatic union illogical?

So is there a magic answer about what exactly makes us irrational, and how those solutions designed for irrational humans are different?
When two irrational numbers are multiplied or divided, the product is sometimes rational and sometimes irrational.
When an irrational number and a rational number are added or subtracted, the sum is irrational.
The product of a rational number and an irrational number is SOMETIMES irrational.
When the square root of an irrational number is taken, does it have to be irrational?
Irrational love and irrational hate jostling together in the heart of that tormented man.
The product of two irrational numbers, in some cases, will be irrational.
Prove or disprove that the product of two irrational numbers is irrational.
Predictably Irrational, behavioral economist Dan Ariely claims that irrational.
The sum of an irrational number and an irrational number is irrational.