In mathematics, a rational number is a number that can be expressed as the quotient or fraction p q {\displaystyle {\tfrac {p}{q}}} of two integers, a...
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In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed...
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number that it represents. In mathematics, the notion of number has been extended over the centuries to include zero (0), negative numbers, rational numbers...
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In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though...
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proof that π cannot be rational; Legendre (1794) completed the proof and showed that π is not the square root of a rational number. Liouville (1840) showed...
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Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the...
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Arithmetic (section Rational number arithmetic)
type of number they operate on. Integer arithmetic restricts itself to calculations with positive and negative whole numbers. Rational number arithmetic...
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An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example...
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numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral...
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In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example...
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Diophantine approximation (redirect from Metrical number theory)
well a real number can be approximated by rational numbers. For this problem, a rational number p/q is a "good" approximation of a real number α if the absolute...
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Fraction (redirect from Rational arithmetic)
rational number (for example 2 2 {\displaystyle \textstyle {\frac {\sqrt {2}}{2}}} ), and even do not represent any number (for example the rational fraction...
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Repeating decimal (redirect from Recurring number)
finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating. It can be shown that a number is rational if...
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transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients...
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Continued fraction (redirect from Best rational approximation)
representation for a real number is finite if and only if it is a rational number. In contrast, the decimal representation of a rational number may be finite, for...
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Look up rational in Wiktionary, the free dictionary. Rational may refer to: Rational number, a number that can be expressed as a ratio of two integers...
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Decimal (redirect from Decimal approximation of a real number)
decimal represents a rational number, the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits....
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primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example...
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numbers that can be more closely approximated by rational numbers than any algebraic irrational number can be. In 1844, Joseph Liouville showed that all...
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Algebraic expression (redirect from Rational equation)
multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression. Since taking...
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Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do...
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mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...
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Integer (redirect from Rational integer)
containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more...
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Factorization (section Rational roots)
{\displaystyle y} is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately...
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of rational numbers Q {\displaystyle \mathbb {Q} } , i.e. 1 Q ( x ) = 1 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=1} if x is a rational number and...
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real number line. This contrasts with the rational numbers, whose corresponding number line has a "gap" at each irrational value. In the decimal number system...
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A schizophrenic number or mock rational number is an irrational number that displays certain characteristics of rational numbers. The Universal Book of...
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is a congruent number—a positive integer that is the area of a right triangle with three rational number sides—and an amenable number. 69 can be expressed...
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{\displaystyle r} is any real number. Although it is feasible to define the value as the limit of a sequence of rational powers that approach the irrational...
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