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A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

Young's geometry is a finite geometry which satisfies the following five axioms: 1. There exists at least one line. 2. Every line of the geometry has exactly three points on ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...