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In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [1] [2] Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side ...
The equals sign (British English) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense. [1] In an equation , it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
An alternative notation for this usage is to typeset the letters "def" above an ordinary equality sign, =. [14] Similarly, another alternative notation for this usage is to precede the equals sign with a colon, :=. The colon notation has the advantage that it reflects the inherent asymmetry in the definition of one object from already defined ...
At the middle- or high-school level, 34 states use a mercy rule that may involve a "continuous clock" (the clock continues to operate on most plays when the clock would normally stop, such as an incomplete pass) once a team has a certain lead (for example, 35 points) during the second half (Louisiana adopted a rule in 2022 which states the running clock is invoked when the margin reaches 42 ...
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.
The figure at the right shows three examples beginning with clear inequality (top) and approaching equality (bottom). In the Euclidean case, equality occurs only if the triangle has a 180° angle and two 0° angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest distance between ...
On Padé approximations to the exponential function and A-stable methods for the numerical solution of initial value problems (PDF) (Thesis). Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems , Berlin, New York: Springer-Verlag , ISBN 978-3-540-56670-0 .