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Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein 's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy ...
A basis (or reference frame) of a (universal) algebra is a function that takes some algebra elements as values () and satisfies either one of the following two equivalent conditions. Here, the set of all b ( i ) {\displaystyle b(i)} is called the basis set , whereas several authors call it the "basis".
The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
The set Γ of all open intervals in forms a basis for the Euclidean topology on .. A non-empty family of subsets of a set X that is closed under finite intersections of two or more sets, which is called a π-system on X, is necessarily a base for a topology on X if and only if it covers X.
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
The use of Unicode characters for blackboard bold is discouraged in English Wikipedia; instead, either the LaTeX rendering (for example <math>\mathbb{Z}</math> or <math>\Z</math>) or standard bold fonts should be used. As with all such choices, each article should be consistent with itself, and editors should not change articles from one choice ...
An asymptotic additive basis is a set for which all but finitely many natural numbers can be expressed as a sum of or fewer elements of . [ 1 ] For example, by Lagrange's four-square theorem , the set of square numbers is an additive basis of order four, and more generally by the Fermat polygonal number theorem the polygonal numbers for k ...
Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000, Lond. Math. Soc. Lect. Note Ser., vol. 310, Cambridge: Cambridge University Press, pp. 145– 189, ISBN 978-0-521-53365-2, Zbl 1051.37007