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- 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 xf.
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".
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- 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!)
- Sn, the symmetric group
(of permutations) over {1,...,n}.
- Z, the integers, { ..., -2, -1, 0, 1, 2, 3, ... }.
- Zn, the integers modulo (mod) n,
{0, 1, ..., n-1}.
- Zp, as above, {0, 1, ..., p-1},
where p is a prime number.
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- ∀, 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.
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- {x | p(x)}, the set of x such that p(x) is true.
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