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Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

A subsequence of {a} is a sequence {b} defined by b_k=a_(n_k), where n_1<n_2<... is an increasing sequence of indices (D'Angelo and West 2000). For example, the prime numbers ...

A condition used in the definition of a mathematical object, commonly denoted : or |. For example, the rationals Q can be defined by Q={p/q:q!=0,p,q in Z}, read as "the set ...

The general function y(a,b,c,d)=csin{pi/(b-a)[((b-a)x/d+a)^2-a^2]}.

A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. An example of a syllogism is modus ponens.

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

A quartic surface given by the implicit equation x^4-5x^2+y^4-5y^2+z^4-5z^2+11.8=0.

One trillion (10^(12)) bytes. Unfortunately, the term is sometimes also used to mean 2^(40)=1024^4=1099511627776 bytes. However, this usage is deprecated, and the term ...