Search Results for ""

A ringoid is a set R with two binary operators, conventionally denoted addition (+) and multiplication (×), where × distributes over + left and right: a(b+c)=ab+ac and ...

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

If {a_0,a_1,...} is a recursive sequence, then the set of all k such that a_k=0 is the union of a finite (possibly empty) set and a finite number (possibly zero) of full ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...

Also called indiscrete topology, the trivial topology is the smallest topology on a set X, namely the one in which the only open sets are the empty set and the entire set X. ...

Algebra

A p-system of a set S is a sequence of subsets A_1, A_2, ..., A_p of S, among which some may be empty or coinciding with each other.

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 ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...