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The theorem extends to the other trigonometric functions as well. [2] For rational values of θ, the only rational values of the sine or cosine are 0, ±1/2, and ±1; the only rational values of the secant or cosecant are ±1 and ±2; and the only rational values of the tangent or cotangent are 0 and ±1. [3]
the population mean or expected value in probability and statistics; a measure in measure theory; micro-, an SI prefix denoting 10 −6 (one millionth) Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning) the coefficient of friction in physics; the service rate in queueing theory
In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point.
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 ...
Fermat's last theorem Fermat's last theorem, one of the most famous and difficult to prove theorems in number theory, states that for any integer n > 2, the equation a n + b n = c n has no positive integer solutions. Fermat's little theorem Fermat's little theorem field extension A field extension L/K is a pair of fields K and L such that K is ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The hyperelliptic curve defined by = (+) (+) has only finitely many rational points (such as the points (,) and (,)) by Faltings's theorem.. In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1]
By Ostrowski's theorem, every non-trivial absolute value on the rational numbers is equivalent to either the usual absolute value or some -adic absolute value. The rational field is not complete with respect to non-trivial absolute values; with respect to the trivial absolute value, the rational field is a discrete topological space, so complete.