Glossary

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), e.g., addition (+) of integers (but not subtraction (-)).
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.t., short for "such that".
N, the natural numbers, {0, 1, 2, 3, ... }.
Q, the rational numbers, {m/n | m∈Z, n∈N-{0}}.
R, the real numbers. (Can't enumerate them!)
S_n, the symmetric group (of permutations) over {1,...,n}.
Z, the integers, { ..., -2, -1, 0, 1, 2, 3, ... }.
Z_n, the integers modulo (mod) n, {0, 1, ..., n-1}.
Z_p, as above, {0, 1, ..., p-1}, where p is a prime number.
∀, for all; also see [logic] and [spec.chars].
∃, there exists.
∧, as in p∧q, p and q, conjunction.
∨, as in p∨q, p or q, disjunction.
¬, as in ¬p, not p, 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, y⟩, ordered pair, note ⟨x, y⟩ ≠ ⟨y, x⟩ in general.
{x | p(x)}, the set of x such that p(x) is true.