Difference between Irrational and Unfounded

IRRATIONAL vs UNFOUNDED: NOUN

That which is devoid of reason, as one of the lower animals.
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.
A prime number.
An irrational number.
A real number that can not be expressed as the quotient of two integers, an irrational number.

Not consistent with or using reason
Not endowed with reason.
Affected by loss of usual or normal mental clarity; incoherent, as from shock.
Marked by a lack of accord with reason or sound judgment.
Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
Being a metric foot containing such a syllable.
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.
Real but not expressible as the quotient of two integers

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 Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.
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.

Not founded; not built or established. Having no foundation; vain; idle; baseless: as, unfounded expectations.

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

Unreasonable, Spurious, Ungrounded, False, Irrational, Inaccurate, Erroneous, Unjustified, Unsubstantiated, Untrue, Idle, Unsupported, Unwarranted, Baseless, Groundless

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

Unreasonable, Spurious, Ungrounded, False, Irrational, Inaccurate, Erroneous, Unjustified, Unsubstantiated, Untrue, Idle, Unsupported, Unwarranted, Baseless, Groundless

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.

Americans feel toward large corporations is not unfounded.
This fear of ethnic secession is not unfounded.
Arab minority living within its borders, are unfounded.
Are Unfounded or Inconclusive Reports Reported to CACI?
Further, his assumption was not an unfounded one.
History has proven those fears to be unfounded.
British subjects might lead to war proved unfounded.
Unfounded: Investigation indicates that the allegations are false.
Eric --- unfounded mail is cushioned polymyositis Free.
Unfounded final determination has the right to request the unfounded case be retained as intentionally false notified medical.