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Caesar's method is an encryption scheme involving shifting an alphabet (so a->c, b->d, c->e, d->f, etc., x->z,y->a,z->b). It is one of the most basic encryption methods, and ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

A floating-point number is a finite or infinite number that is representable in a floating-point format, i.e., a floating-point representation that is not a NaN. In the IEEE ...

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...