Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems: The "primary arithmetic" (described in Chapter 4 of LoF), whose models include Boolean arithmetic; The "primary algebra" (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; "Equations of the second degree" (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive...

Bézout's identity (also called Bézout's lemma) is a theorem in elementary number theory: let a and b be nonzero integers and let d be their greatest common divisor. Then there exist integers x and y such that a x + b y = d . {\displaystyle ax+by=d.} In addition, the greatest common divisor d is the smallest positive integer that can be written as ax + by every integer of the form ax + by is a multiple of the greatest common divisor d. The integers x and y are called Bézout coefficients for (a, b)...

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable. An important source of metrics in differential geometry are metric tensors, bilinear forms that may be defined from the tangent vectors of a differentiable manifold onto a scalar. A metric tensor allows distances along curves to be determined through...

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable. An important source of metrics in differential geometry are metric tensors, bilinear forms that may be defined from the tangent vectors of a differentiable manifold onto a scalar. A metric tensor allows distances along curves to be determined through...