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...

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed...

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...

number that it represents. In mathematics, the notion of number has been extended over the centuries to include zero (0), negative numbers, rational numbers...

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...

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...

type of number they operate on. Integer arithmetic restricts itself to calculations with positive and negative whole numbers. Rational number arithmetic...

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...

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...

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...

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...

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...

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...

rational number (for example 2 2 {\displaystyle \textstyle {\frac {\sqrt {2}}{2}}} ), and even do not represent any number (for example the rational fraction...

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...

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...

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....

multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression. Since taking...

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...

numbers that can be more closely approximated by rational numbers than any algebraic irrational number can be. In 1844, Joseph Liouville showed that all...

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...

of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result...

containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more...

mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...

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...

{\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...

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...

A schizophrenic number or mock rational number is an irrational number that displays certain characteristics of rational numbers. The Universal Book of...

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...

\mathbb {Q} } ): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit i {\displaystyle...