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The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]
The CPT theorem can be generalized to take into account pin groups. In 2002 Oscar Greenberg proved that, with reasonable assumptions, CPT violation implies the breaking of Lorentz symmetry. [9] CPT violations would be expected by some string theory models, as well as by some other models that lie outside point-particle quantum field theory.
Cameron–Erdős theorem (discrete mathematics) Cameron–Martin theorem (measure theory) Cantor–Bernstein–Schroeder theorem (set theory, cardinal numbers) Cantor's intersection theorem (real analysis) Cantor's isomorphism theorem (order theory) Cantor's theorem (set theory, Cantor's diagonal argument)
Pages in category "Theorems in computational complexity theory" The following 22 pages are in this category, out of 22 total. This list may not reflect recent changes. B.
Erdős–Beck theorem: Mathematics: Paul Erdős and József Beck: Erdős–Gallai theorem: Mathematics: Paul Erdős and Tibor Gallai: Erdős–Kac theorem: Mathematics: Paul Erdős and Mark Kac: Erdős–Ko–Rado theorem: Mathematics: Paul Erdős, Ke Zhao, and Richard Rado: Erdős–Nagy theorem: Mathematics: Paul Erdős and Béla Szőkefalvi ...
Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that
The intermediate value theorem is an existence theorem, based on the real number property of completeness, and states: If the real-valued function f is continuous on the closed interval [ a , b ] , {\displaystyle [a,b],} and k is some number between f ( a ) {\displaystyle f(a)} and f ( b ) , {\displaystyle f(b),} then there is some number c ∈ ...
In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]