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In the social sciences, the word "clique" is used to describe a group of 3 to 12 "who interact with each other more regularly and intensely than others in the same setting". [1] Cliques are distinguished from " crowds " in that their members socially interact with one another more than the typical crowd (e.g. hang out together, go shopping ...
The 11 light blue triangles form maximal cliques. The two dark blue 4-cliques are both maximum and maximal, and the clique number of the graph is 4. In graph theory, a clique (/ ˈ k l iː k / or / ˈ k l ɪ k /) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent.
The commutator subgroup of a free group of rank k > 1 has infinite rank; for example for F(a,b), it is freely generated by the commutators [a m, b n] for non-zero m and n. The free group in two elements is SQ universal; the above follows as any SQ universal group has subgroups of all countable ranks. Any group that acts on a tree, freely and ...
A worksheet, in the word's original meaning, is a sheet of paper on which one performs work. They come in many forms, most commonly associated with children's school work assignments, tax forms, and accounting or other business environments. Software is increasingly taking over the paper-based worksheet.
The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.
Elementary arithmetic aims to give students a basic sense of numbers and to familiarize them with fundamental numerical operations like addition, subtraction, multiplication, and division. [185] It is usually introduced in relation to concrete scenarios, like counting beads , dividing the class into groups of children of the same size, and ...
For the real quadratic field = (with d square-free), the fundamental unit ε is commonly normalized so that ε > 1 (as a real number). Then it is uniquely characterized as the minimal unit among those that are greater than 1. If Δ denotes the discriminant of K, then the fundamental unit is
The definition of multiplication is a part of all these definitions. A fundamental aspect of these definitions is that every real number can be approximated to any accuracy by rational numbers. A standard way for expressing this is that every real number is the least upper bound of a set of rational numbers.
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