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The rule (F,F=>G)/G, where => means "implies," which is the sole rule of inference in propositional calculus. This rule states that if each of F and F=>G is either an axiom ...

Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j ...

A multilinear form on a vector space V(F) over a field F is a map f:V(F)×...×V(F)->F (1) such that c·f(u_1,...,u_i,...,u_n)=f(u_1,...,c·u_i,...,u_n) (2) and ...

The symbol × used to denote multiplication, i.e., a×b denotes a times b. The symbol × is also used to denote a group direct product, a Cartesian product, or a direct product ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...

Let f:R->R, then the negative part of f is the function f^-:R->R defined by f^-(x)=max(-f(x),0). Note that the negative part is itself a nonnegative function. The negative ...