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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 + irrational = rational - Physics Forums
    Can someone prove that there exists x and y which are elements of the reals such that x and y are irrational but x+y is rational? Certainly, there are an infinite number of examples (pi 4 + -pi 4 for example) to show this, but how would you prove the general case?
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  • Is the Square Root of Pi Irrational? - Physics Forums
    The proof shows that if pi is irrational then so is its square root Presumably that is what the question asked, or intended to ask
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    Find a sequence of rational numbers that converges to the square root of 2
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    I'm sure that a proof for something like this would be easier with an algebraic number, but how would you do so for a transcendental number like e or pi or tau? So my main point is, theoretically, shouldn't all numbers, including irrational and transcendental, repeat? Or is it just an absence of a proof that causes this to be false?
  • Can one use an irrational number as a base? - Physics Forums
    Can one make an irrational number rational by defining it as the unit of a counting system? I don't know what constitutes an mathematically consistent 'number line' - this question might not make sense I'm just thinking that if I use pi as my unit, can write pi as a rational number, since 1 is a rational number
  • If a, b are irrational, then is - Physics Forums
    Homework Statement True or false and why: If a and b are irrational, then is irrational Homework Equations None, but the relevant example provided in the text is the proof of irrationality of The Attempt at a Solution Attempt proof by contradiction Say is rational, then we can express for some integer c and d





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