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The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice. Renteln ...

Trigonometry

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...