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Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

Define the sequence a_0=1, a_1=x, and a_n=(a_(n-2))/(1+a_(n-1)) (1) for n>=0. The first few values are a_2 = 1/(1+x) (2) a_3 = (x(1+x))/(2+x) (3) a_4 = ...

The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

In the early 1960s, B. Birch and H. P. F. Swinnerton-Dyer conjectured that if a given elliptic curve has an infinite number of solutions, then the associated L-series has ...

von Neumann-Bernays-Gödel set theory (abbreviated "NBG") is a version of set theory which was designed to give the same results as Zermelo-Fraenkel set theory, but in a more ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...