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In mathematics real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra. The word is also used as a noun, meaning a real number (as in "the set of all reals").
A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of, [22] [23] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see § Multiplication ).
Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
For example, any irrational number x, such as x = √ 2, is a "gap" in the rationals Q in the sense that it is a real number that can be approximated arbitrarily closely by rational numbers p/q, in the sense that distance of x and p/q given by the absolute value | x − p/q | is as small as desired. The following table lists some examples of ...
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...
Graph of the fractional part of real numbers The fractional part or decimal part [ 1 ] of a non‐negative real number x {\displaystyle x} is the excess beyond that number's integer part . The latter is defined as the largest integer not greater than x , called floor of x or ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } .
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
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