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Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...

Simply stated, floating-point algebra is algebra performed on floating-point representations by any number of automated devices. Traditionally, this definition is phrased so ...

Gödel's first incompleteness theorem states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...

A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

Tracing through the connections of a branchial graph gives rise to the notion of a kind of space in which states on different branches of history are laid out. In particular, ...

A self-organizing data structure which uses rotations to move any accessed key to the root. This leaves recently accessed nodes near the top of the tree, making them very ...