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irrational    音标拼音: [ɪr'æʃənəl]
n. 无理数
a. 无理性的,不合理的

无理数无理性的,不合理的

irrational
adj 1: not consistent with or using reason; "irrational fears";
"irrational animals" [ant: {rational}]
2: real but not expressible as the quotient of two integers;
"irrational numbers" [ant: {rational}]
n 1: a real number that cannot be expressed as a rational number
[synonym: {irrational number}, {irrational}]

irrational \ir*ra"tion*al\ ([i^]r*r[a^]sh"[u^]n*al), a. [L.
irrationalis: cf. F. irrationnel. See {In-} not, and
{Rational}.]
[1913 Webster]
1. Not rational; void of reason or understanding; as, brutes
are irrational animals.
[1913 Webster]

2. Not according to reason; having no rational basis; clearly
contrary to reason; easily disproved by reasoning; absurd;
-- of assertions and beliefs. Hence, of actions: foolish;
unreasonable.
[1913 Webster PJC]

It seemed utterly irrational any longer to maintain
it. --I. Taylor.
[1913 Webster]

3. (Math.) Not capable of being exactly expressed by an
integral number, nor by a ratio of integral numbers; surd;
-- said especially of roots. See {Surd}.

Syn: Absurd; foolish; preposterous; unreasonable; senseless.
See {Absurd}.
[1913 Webster]

185 Moby Thesaurus words for "irrational":
abnormal, absonant, algorismic, algorithmic, aliquot,
bereft of reason, bigoted, brainless, brainsick, cardinal,
contradictory, contrary to reason, crackbrained, cracked, crazed,
crazy, daft, decimal, deluded, demented, deprived of reason,
deranged, differential, digital, disoriented, distraught, even,
exponential, extravagant, extreme, extremist, fallacious, fanatic,
faulty, figural, figurate, figurative, finite, flawed, flighty,
foolish, fractional, haggard, hallucinated, headless, ignorant,
ill-advised, ill-considered, ill-contrived, ill-devised,
ill-gauged, ill-judged, illogical, imaginary, impair, impolitic,
impossible, imprudent, inadvisable, inauthentic, inconclusive,
incongruous, inconsequent, inconsequential, inconsiderate,
inconsistent, indiscreet, inept, inexpedient, infinite,
injudicious, inordinate, insane, insensate, integral, invalid,
lackbrained, lean-minded, lean-witted, loco, logarithmic,
logometric, loose, lunatic, mad, maddened, manic, mazed, mental,
mentally deficient, meshuggah, mindless, misadvised, misguided,
moon-struck, myopic, negative, non compos, non compos mentis,
nonrational, nonscientific, not all there, not bright,
not following, not right, numeral, numerary, numerative, numeric,
odd, of little brain, of unsound mind, off, ordinal,
overenthusiastic, overreligious, overzealous, pair, paralogical,
pea-brained, perfervid, pin-brained, positive, possible, prime,
psycho, queer, rabid, radical, rational, real, reasonless,
reciprocal, reckless, self-annulling, self-contradictory,
self-refuting, senseless, shortsighted, sick, slackminded,
slackwitted, sophistic, stark-mad, stark-staring mad, strange,
submultiple, surd, tetched, thoughtless, touched, transcendental,
ultrazealous, unadvised, unauthentic, unbalanced, unconnected,
unconsidered, undiscerning, unforeseeing, ungifted, unhinged,
unintellectual, unintelligent, unphilosophical, unreasonable,
unreasoning, unreflecting, unreflective, unsane, unscientific,
unseeing, unsensible, unsettled, unsound, untalented, unthinking,
unthoughtful, unwise, wandering, wild-eyed, wild-looking,
without reason, witless, zealotic


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  • irrational = rational - Physics Forums
    One participant proposes a general case involving the difference between a rational number and an irrational number being irrational, suggesting this leads to the conclusion that the sum of two irrational numbers can be rational
  • How Do We Know If Irrational or Transcendental Numbers Repeat?
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  • Proving √n Irrational: A Proof by Contradiction - Physics Forums
    The problem reads as follows: Let n be a positive integer that is not a perfect square Prove that √n is irrational I understand the basic outline that a proof would have Assume √n is rational and use a proof by contradiction We can set √n=p q where p and q are integers with gcd(p,q)=1
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    The discussion revolves around the nature of irrational numbers, specifically questioning whether they are infinite or merely unmeasurable Participants explore the concept of irrational numbers through examples and mathematical reasoning, touching on their representation and approximation in decimal form
  • Is a non-repeating and non-terminating decimal always an irrational . . .
    A non-repeating and non-terminating decimal is always classified as an irrational number, as it cannot be expressed as the ratio of two integers The discussion highlights the decimal representation of numbers like 1 33, which is repeating, versus the nature of irrational numbers such as π, which can be approximated to any number of decimal
  • Irrational Number Raised To Irrational Number - Physics Forums
    The discussion revolves around whether an irrational number raised to an irrational power can yield a rational result The original poster presents a specific case involving \ ( A = (\sqrt {2})^ {\sqrt {2}} \) and explores the implications of whether \ ( A \) is rational or irrational Exploratory, Assumption checking, Conceptual clarification Participants discuss the nature of \ ( A \) and
  • If a, b are irrational, then is - Physics Forums
    The discussion revolves around the question of whether the expression \ ( a^b \) is irrational when both \ ( a \) and \ ( b \) are irrational numbers Participants reference examples and theorems related to irrationality, particularly focusing on the implications of raising irrational numbers to powers Exploratory, Conceptual clarification, Assumption checking Several participants attempt





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