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The set of numbers generated by excluding the sums of two or more consecutive earlier members is called the prime numbers of measurement, or sometimes the segmented numbers. ...

Given a Lucas sequence with parameters P and Q, discriminant D!=0, and roots a and b, the Sylvester cyclotomic numbers are Q_n=product_(r)(a-zeta^rb), (1) where ...

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...

A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

Gödel's second incompleteness theorem states no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. Stated more colloquially, any ...

The conjugate gradient method can be applied on the normal equations. The CGNE and CGNR methods are variants of this approach that are the simplest methods for nonsymmetric ...

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

The set of all zero-systems of a group G is denoted B(G) and is called the block monoid of G since it forms a commutative monoid under the operation of zero-system addition ...