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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
    Assume that the difference between a rational number and an irrational number is an irrational number The sum of any such two irrational numbers would be a rational number All we have to do now is prove the assumption, which I think is easier edit: I just saw tongos' proposition, which I think is better than mine
  • Square Root of an Irrational Number is Irrational - Physics Forums
    By contraposition, if a is irrational then √a is irrational QED There's no need to look at the inverse of "if a is irrational then √a is irrational" and find a contradiction because the two statements "if √a is rational then a is rational" and "if a is irrational then √a is irrational" are one and the same, just worded differently
  • If a, b are irrational, then is ##a^b## irrational? - Physics Forums
    True or false and why: If a and b are irrational, then ##a^b## is irrational Homework Equations None, but the relevant example provided in the text is the proof of irrationality of ##\sqrt{2}## The Attempt at a Solution Attempt proof by contradiction Say ##a^b## is rational, then we can express ##a^b = \frac{c}{d}## for some integer c and d
  • Constructing Lengths with Irrational Numbers - Physics Forums
    By the way, abstract mathematics is inconsistent in that they treat irrational numbers as being both, infinite decimal expansions, and precise calculus limits In other words, Cantor's famous diagonal proof that the set of real numbers has a larger cardinality than the set of natural numbers depends on the infinite expansion of decimal numbers
  • Is the Square Root of Pi Irrational? - Physics Forums
    A question in my book says to prove that pi is irrational, I found a proof which I'm happy with and found a similar one on the web however on the solutions they have done: assume √π is rational i e [tex] \sqrt{\pi} = \frac{p}{q} p,q \in \mathbb{Z} [ tex] [tex] \pi = \frac{p^2}{q^2}, p^2,q^2 \in \mathbb{Z} ∴ \pi \mathrm{is\ rational} [ tex]
  • Irrational numbers arent infinite. are they? - Physics Forums
    There are an infinite number of irrational numbers just as there are an infinite number of integers, rational numbers and real numbers However since reals are uncountable and rationals are countable then irrationals are uncountable meaning there are many more irrationals than rationals
  • Irrational numbers vs. Transcendental numbers - Physics Forums
    Irrational means 'cannot be expressed as a fraction' For example [tex]\sqrt{2}[ tex] is an irrational number Transcendental means is not a solution to any equation that contains only rational numbers For example, [tex]\pi[ tex] is a transcendental number [tex]\sqrt{2}[ tex] is not a transcendental number
  • Sequence of rationals that converge to irrational - Physics Forums
    Find a sequence of rational numbers that converges to the square root of 2
  • How Do We Know If Irrational or Transcendental Numbers Repeat?
    We can ignore the integer part of the number without changing whether it is rational or irrational, so let's just focus on the digits to the right of the decimal If they are ##a_1 a_2 \ldots a_N a_1 a_2 \ldots a_N \ldots## then this is equal to
  • Can one use an irrational number as a base? - Physics Forums
    All numbers, including integers, rational numbers, and irrational numbers, are defined independently of any numeration system I kind of get that, but I am missing what a rational number is, I think If I take and lay straight a rope of unit length in the base 1 number line, I can then cut a rope that is the length of the circle enclosing the





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