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The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts.
The two-element subset {3, 5} is a generating set, since (−5) + 3 + 3 = 1 (in fact, any pair of coprime numbers is, as a consequence of Bézout's identity). The dihedral group of an n-gon (which has order 2n ) is generated by the set { r , s } , where r represents rotation by 2 π / n and s is any reflection across a line of symmetry.
The manipulations of the Rubik's Cube form the Rubik's Cube group.. In mathematics, a group is a set with an operation that associates every pair of elements of the set to an element of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.
Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. [2] [3]
The reason s 2 and not s is called the interval is that s 2 can be positive, zero or negative. Spacetime intervals may be classified into three distinct types, based on whether the temporal separation (c 2 Δt 2) or the spatial separation (Δr 2) of the two events is greater: time-like, light-like or space-like.
In the Algebra preface of his book, Precalculus Mathematics in a Nutshell, Professor George F. Simmons wrote that the New Math produced students who had "heard of the commutative law, but did not know the multiplication table". [5] In 1965, physicist Richard Feynman wrote in the essay, New Textbooks for the "New" Mathematics:
The 7.5×55mm Swiss / GP 11 cartridge (designated as the 7.5 × 55 Suisse by the C.I.P.) [8] has 4.22 ml (65 grains) H 2 O cartridge case capacity. The exterior shape of the case was designed to promote reliable case feeding and extraction in bolt-action rifles and machine guns alike, under extreme conditions.
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