For S-semimodules MS and SN, their tensor product M[cross product]N is defined as the factor semigroup of the free commutative additive semigroup F=F(M x N) generated by the set M x N, factorized by the congruence [rho] generated by all ordered pairs
of the form
For example, 7 [congruent to] 2 (mod 5) and 1 [congruent to] 13 (mod 3) Define sets, [R.sub.a,b] consisting of ordered pairs
and a singleton defined by:
These ordered pairs
indicate that a is mapped to y and a is mapped to z.
Digraph D consists of a finite set V of points (vertex) and a collection of ordered pairs
of distinct points.
When the input is a function, then the function is considered as the set of ordered pairs
. In other words, y = f(x) is considered as the set of all points (x, f (x)).
In accordance with the definition by Sidman (2000), "the equivalence relation consists of ordered pairs
of all positive elements that participate in the reinforcement contingency" (Sidman 2000, p.
(ii) The first element in the ordered pairs
of 1-hop list is the sensor itself.
Mathematical concepts that are taught include how to plot data points from a table, how to label ordered pairs
, and how to name coordinates on a grid.
But the actualist transformation-method allows actualists armed with the dot-notation to follow suit, by quantifying over a-worlds and ordered pairs
Let us partition the set of odd-sized orbits of [gamma] into ordered pairs
and let ([O.sub.1],O2) be such a pair.
The notions of tonal "qualia" and "chroma" lie at the heart of the tonal GIS, which Rings represents as ordered pairs
of' scale degrees and pitch classes (sd, pc) respectively.
Written as ordered pairs
(x, y) according to Table 1, the coordinates of the stars are as follows: Atlas (66, 400); Alcyone (204, 468); Merope (224, 793); Maia (249, 336); Taygeta (488, 315); Electra (508, 858); and Celaeno (618, 640).