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However, the equality of two real numbers given by an expression is known to be undecidable (specifically, real numbers defined by expressions involving the integers, the basic arithmetic operations, the logarithm and the exponential function). In other words, there cannot exist any algorithm for deciding such an equality (see Richardson's theorem
Galileo's law of odd numbers. A ramification of the difference of consecutive squares, Galileo's law of odd numbers states that the distance covered by an object falling without resistance in uniform gravity in successive equal time intervals is linearly proportional to the odd numbers. That is, if a body falling from rest covers a certain ...
The solution set of the equation x 2 / 4 + y 2 = 1 forms an ellipse when interpreted as a set of Cartesian coordinate pairs. Main article: Solution set The solution set of a given set of equations or inequalities is the set of all its solutions, a solution being a tuple of values, one for each unknown , that satisfies all the equations ...
Mean value: If x is a variable that takes its values in some sequence of numbers S, then ¯ may denote the mean of the elements of S. 5. Negation : Sometimes used to denote negation of the entire expression under the bar, particularly when dealing with Boolean algebra .
If x is a nonnegative real number, and n is a positive integer, / or denotes the unique nonnegative real n th root of x, that is, the unique nonnegative real number y such that =. If x is a positive real number, and p q {\displaystyle {\frac {p}{q}}} is a rational number , with p and q > 0 integers, then x p / q {\textstyle x^{p/q}} is defined as
As a theme and as a subject in the arts, the anti-intellectual slogan 2 + 2 = 5 pre-dates Orwell and has produced literature, such as Deux et deux font cinq (Two and Two Make Five), written in 1895 by Alphonse Allais, which is a collection of absurdist short stories; [1] and the 1920 imagist art manifesto 2 × 2 = 5 by the poet Vadim Shershenevich.
The set of solutions of a real linear inequality constitutes a half-space of the 'n'-dimensional real space, one of the two defined by the corresponding linear equation. The set of solutions of a system of linear inequalities corresponds to the intersection of the half-spaces defined by individual inequalities.
The lack of real square roots for the negative numbers can be used to expand the real number system to the complex numbers, by postulating the imaginary unit i, which is one of the square roots of −1. The property "every non-negative real number is a square" has been generalized to the notion of a real closed field, which is an ordered field ...