Maths Glossary

Application, f(x), of a function, f, to an actual parameter, x. May also be written as f x, or as postfix, x f, or even as x^f. Also see composition.

Associative, where a binary operation, '·', satisfies (a · b) · c = a · (b · c).

Commutative, where a binary operation, '·', satisfies a · b = b · a, for all appropriate a and b, e.g., addition (+) of integers.

Composition, f·g, of functions g:X→Y and f:Y→Z, (f·g)(x) = f(g(x)), f·g:X→Z; apply g first and then f. Note that composition is associative, (f·g)·h = f·(g·h). (f·g is sometimes written as fg, and sometimes as postfix g;f, or even gf!) Also see application.

Graph, see [here].

Group, see [here].

iff, short for "if and only if".

S_n, the symmetric group (of permutations) over {1,...,n}.

s.t., short for "such that".

Z, the integers, ...,-2,-1,0,1,2,3,... .

Z_n, the integers modulo (mod) n, {0, 1, ..., n-1}.

 

&forall, for all; see [spec.chars].

&exist, there exists.

∧, as in p∧q, p and q, conjunction.

∨, as in p∨q, p or q, disjunction.

¬, as in ¬p, not, logical negation.

∈, as in x∈S, x is a member of S.

∩, as in S∩T, set intersection.

∪, as in S∪T, set union.

|x|, the size of x, the length of a sequence or string, the number of elements in a set, etc..

[y,z] = {x | y ≤ x ≤ z}, closed interval.

[y,z) = {x | y ≤ x < z}, half closed interval.

(y,z] = {x | y < x ≤ z}, half closed interval.

(y,z) = {x | y < x < z}, open interval (but also unordered pair in other contexts).

 

{x | p(x)}, the set of x such that p(x) is true.