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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
  • 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 Pi divided by E rational, and what other irrational numbers exist?
    Does anyone know if it has ever been proved that pi divided e, added to e, or any other mathematical operation combining these two irrational numbers is rational Another thing does anybody know of any other irrational numbers that is not some derivative of pi and e
  • Factoring irrational equations - Physics Forums
    However, if "0" does not appear, then the number in the brackets is not a value of x, so you must choose from the list of numbers (the ±1, ±5 3, ±1 3, ±5) However, after going through every possible number in that list, none ever got to "0" which means that the equation does not have any rational numbers (so the answer must be irrational)
  • Is sqrt(5) Rational? Understanding the Proof by Contradiction
    6 is a natural number six can be composed as 2*3 2 and 3 are primes, so the SQRT of a prime is irrational since a prime has no factors other than itself and 1 if you multiply the root of 2 distict prime numbers together, you end up with an irrational number, and since SQRT(6) can be composed as SQRT(2*3) and since we know that the SQRT of 2
  • Irrational number to an irrational power - Physics Forums
    But as for the original question, this is a well-known proof that's often cited as a classic non-constructive proof The proposition is that an irrational raised to an irrational power can be rational So we consider ##x = \sqrt{2}^\sqrt{2}## Either ##x## is rational or irrational If it's the former, our work is done
  • Proving Root n is Irrational: Perfect Square Affects Proof - Physics Forums
    n divides q^2, therefore n divides q Now n is a common factor for p q But we know that p q are co-prime Hence our assumption is wrong, root n is irrational 2) if n is a composite Let's say it is product of two primes c1 c2 The proof remains the same for any number of primes
  • 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
  • Is Pi a rational number in any other base besides base Pi? - Physics Forums
    I was thinking about how some binary fractions appear as irrational that would be rational in base 10 Then I wondered if there was any case of the opposite where an irrational number could appear rational in another base, specifically Pi
  • Is there always at least one irrational number between any two rational . . .
    Therefore, an irrational number in I_2 is 1 root2 + p q Therefore, within any interval [a,b], there is at least one irrational number And, also, since there are an infinite amount of subintervals within any interval, with each subinterval having at least one irrational number, then there are an infinite amount of irrational numbers in any





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