The difference between Arational and Rational
When used as adjectives, arational means not within the domain of what can be understood or analyzed by reason, whereas rational means capable of reasoning.
Rational is also noun with the meaning: a rational number: a number that can be expressed as the quotient of two integers.
check bellow for the other definitions of Arational and Rational
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Arational as an adjective (chiefly, philosophy):
Not within the domain of what can be understood or analyzed by reason; not rational, outside the competence of the rules of reason.
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Rational as an adjective:
Capable of reasoning.
Examples:
"Man is a rational creature."
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Rational as an adjective:
Logically sound; not contradictory or otherwise absurd.
Examples:
"His statements were quite rational."
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Rational as an adjective (of a person or personal characteristics):
Healthy or balanced intellectually; exhibiting reasonableness.
Examples:
"'rational conduct"
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Rational as an adjective (mathematics, arithmetic, number theory, not comparable):
Of a number, capable of being expressed as the ratio of two integers.
Examples:
"¾ is a rational number, but √<span style="text-decoration:overline">2</span> is an irrational number."
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Rational as an adjective (mathematics, arithmetic, not comparable):
Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
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Rational as an adjective (chemistry):
Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
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Rational as an adjective (physics):
Expressing a physical object.
Examples:
"A rational table is physical, a written table is neither."
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Rational as a noun (mathematics):
A rational number: a number that can be expressed as the quotient of two integers.
Examples:
"The quotient of two rationals is again a rational."
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Rational as a noun (historical):
The breastplate worn by Israelite high priests.
Examples:
"'1609, Douay-Rheims Bible, Exodus 28:15"
"And thou shalt make the rational of judgment with embroidered work of divers colours, according to the workmanship of the ephod, of gold, violet, and purple, and scarlet twice dyed, and fine twisted linen."