How To Use Rational number In A Sentence
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The standards of rigour that he set, defining, for example, irrational numbers as limits of convergent series, strongly affected the future of mathematics.
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the set of all rational numbers is a field
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Combining with his proof of the denumerability of rational numbers, it proves the existence of irrational numbers without actually constructing any irrational number.
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The set of rational numbers is denumerable, that is, it has cardinal number d.
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the set of all rational numbers is a field
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He knew that when some irrational number produced a very large quotient then it could be rationalised to produce an extremely accurate approximation to some irrational.
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A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients.
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This is an aberrational number of deaths in such a short period.
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The square root of 2 is an irrational number because it can't be written as a ratio of two integers.
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irrational numbers
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The first, and perhaps most definitive, indication that the later Wittgenstein maintains his finitism is his continued and consistent insistence that irrational numbers are rules for constructing finite expansions, not infinite mathematical extensions.
Wittgenstein's Philosophy of Mathematics
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One of my more distinct recollections of math class involves the decimal representation of rational numbers and the discovery of wonderful patterns among those digits.
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For example, the Pythagoreans did not expect to uncover irrational numbers in the diagonal of a square.
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What about a seed angle derived from the golden ratio, an irrational number?
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The converse is also true, i.e. that every rational number has a decimal fraction that either stops or eventually repeats the same cycle of digits over and over again for ever.
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He considered computation with irrational numbers and polynomials to be part of algebra.
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This code is for finding an rational number complete source code, has been tested.
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In particular he strongly criticised Cantor's and Dedekind's theories of irrational numbers.
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His idea was that every real number r divides the rational numbers into two subsets, namely those greater than r and those less than r.
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He considered computation with irrational numbers and polynomials to be part of algebra.
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The very names negative numbers, irrational numbers, transcendental numbers, imaginary numbers, and ideal points at infinity indicate ambivalence.
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Cantor published a paper on trigonometric series in 1872 in which he defined irrational numbers in terms of convergent sequences of rational numbers.
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His idea was that every real number r divides the rational numbers into two subsets, namely those greater than r and those less than r.
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We could add any individual real number to the set of rational numbers and still have a countable collection, just as we may be able to prove individual problems from a non-algorithmic class of problems.
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Irrational numbers are numbers that can be written as decimals but not as fractions.
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rational numbers
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Given that, we are done for rational numbers whose denominator is relatively prime to 10 (i.e. has no factors of 5 or 2), by the opposite of the method in my earlier post.
The Volokh Conspiracy » Pi Day
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An example of something that is uncountably infinite would be all the real numbers (including numbers like 2.34… and the square root of 2, as well as all the integers and rational numbers).
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When the coefficients of quadratic equations were irrational numbers, Abu Kdmil abandoned the geometry demonstration showing the trend of arithmetization.
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“Since all theorems of applied mathematics are deducible from the subsystem [of physical interpretation of the field of rational numbers] ¦ it is only this subsystem which is verified by the interpretations.” (1978, vol. I, p. 423) So we cannot empirically confirm any claims that are properly about real or complex numbers, so we cannot empirically confirm their consistency.
Hans Reichenbach
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If you stop at this point, you will have a rational number that is very close to the decimal F.
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How can mathematical concepts like points, infinitesimally small quantities, or irrational numbers be anything but products of our minds?
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They are not irrational numbers according to Wittgenstein's criteria, which define, Wittgenstein interestingly asserts, “precisely what has been meant or looked for under the name ˜irrational number™” (PR §191).
Wittgenstein's Philosophy of Mathematics
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This theory holds for all irrational numbers
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He considered computation with irrational numbers and polynomials to be part of algebra.
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Term formalism can perhaps be extended to the integers and rational numbers, but what are the real numbers supposed to be?
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Book 3 contains a description of how to carry out arithmetic with irrational numbers.
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The need for rationalization arises when there are irrational numbers, surds or roots or complex numbers in the denominator of a fraction.
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A phaenomenon that is a clear consequence of the theory of irrational numbers.
Red State Rabble on the dangers of the Discovery Institute's Plan B - The Panda's Thumb
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Boutroux's topics range from rational numbers to an analysis of the notion of a function.
