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Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

A pattern tau=(tau_1,...,tau_n) is said to avoid alpha=(alpha_1,...,alpha_k) if alpha is not contained in tau. In other words, tau avoids alpha iff no k-subset of tau is ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

A flow defined analogously to the axiom A diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

Axiomatic set theory is a version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths.

A logical system which possesses an explicitly stated set of axioms from which theorems can be derived.

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...