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The Barnes Opening (sometimes called Gedult's Opening) is a chess opening where White opens with: . 1. f3. The opening is named after Thomas Wilson Barnes (1825–1874), an English player who had an impressive [1] eight wins over Paul Morphy, including one game where Barnes answered 1.e4 with 1...f6, known as the Barnes Defence.
The Zukertort Opening is a chess opening named after Johannes Zukertort that begins with the move: . 1. Nf3. Sometimes the name "Réti Opening" is used for the opening move 1.Nf3, [1] although most sources define the Réti more narrowly as the sequence 1.Nf3 d5 2.c4.
It is now almost universally used by books, magazines, newspapers and software, and is the only form of notation recognized by FIDE, [2] the international chess governing body. An early form of algebraic notation was invented by the Syrian player Philip Stamma in the 18th century.
The reversed order of composition in the formula (f ∘ g) −1 = (g −1 ∘ f −1) applies for composition of relations using converse relations, and thus in group theory. These structures form dagger categories. The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by ...
In mathematics, the free group F S over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st = suu −1 t but s ≠ t −1 for s,t,u ∈ S). The members of S are called generators of F S, and the number of generators is the ...
Textbooks written in Pashto distributed to Afghan school children. A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners (who could be independent learners ...
f(X) = X n + a n−1 X n−1 + ⋯ + a 0 (where f is regarded as a polynomial in E(a 0, ..., a n−1), for some indeterminates a i, E is any field, and n ≥ 5). The tensor product of fields is not usually a field. For example, a finite extension F / E of degree n is a Galois extension if and only if there is an isomorphism of F-algebras F ⊗ ...
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]