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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 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Some programming languages provide a built-in (primitive) rational data type to represent rational numbers like 1/3 and −11/17 without rounding, and to do arithmetic on them. Examples are the ratio type of Common Lisp , and analogous types provided by most languages for algebraic computation , such as Mathematica and Maple .
A stronger result is the following: [31] Every rational number in the interval ((/) /,) can be written either as a a for some irrational number a or as n n for some natural number n. Similarly, [ 31 ] every positive rational number can be written either as a a a {\displaystyle a^{a^{a}}} for some irrational number a or as n n n {\displaystyle n ...
The rational root theorem (or integer root theorem) may be used to show that any square root of any natural number that is not a perfect square is irrational. For other proofs that the square root of any non-square natural number is irrational, see Quadratic irrational number or Infinite descent.
Rational approximation may refer to: Diophantine approximation , the approximation of real numbers by rational numbers Padé approximation , the approximation of functions obtained by set of Padé approximants
The 'rise-to-run' ratio of the stepped faces of the crystal was a simple rational number p/q, where p and q are small multiples of units of length (generally different and not more than 6). [6]: 46 [11] Haüy's method is named the law of decrements, law of simple rational truncations, or Haüy's law.
These are called dyadic numbers and have the form m / 2 n where m is an odd integer and n is a natural number. Put these numbers in the sequence: r = (1/2, 1/4, 3/4, 1/8, 3/8, 5/8, 7/8, ...). Also, f 2 ( t ) is not a bijection to (0, 1) for the strings in T appearing after the binary point in the binary expansions of 0, 1, and the numbers in ...