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An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...

Various handshaking problems are in circulation, the most common one being the following. In a room of n people, how many different handshakes are possible? The answer is (n; ...

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...

The inverse limit of a family of R-modules is the dual notion of a direct limit and is characterized by the following mapping property. For a directed set I and a family of ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

A number x such that for all epsilon>0, there exists a member of the set y different from x such that |y-x|<epsilon. The topological definition of limit point P of A is that ...

A point x^* which is mapped to itself under a map G, so that x^*=G(x^*). Such points are sometimes also called invariant points or fixed elements (Woods 1961). Stable fixed ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. Also known as an indirect ...