Table of symbols
Appendix 11. Table of symbols
Symbol | Reference |
---|---|
￢ | negation |
∧ | conjunction |
∨ | disjunction |
⇒, ⇔ | implication |
∼ | equivalence relation |
∃, ∀ | quantifier |
∈, ∉ | belongs to, does not belong to |
⊆, ⊇ | subset |
⊂, ⊃ | proper subset |
∪, ⋃ | union |
∩, ⋂ | intersection |
A′, Ā | complement |
∅ | empty set |
A×B | Cartesian product |
A \ B, A−B | difference set |
A+B, A Δ B | symmetric difference |
n(A), # (A), |A| | cardinality |
℘(A) | power set |
n! | factorial |
[a, b] | closed interval, least common multiple |
(a, b) | open interval, greatest common divisor |
[a, b), (a, b] | interval, open at one end |
binomial coefficient | |
[x] | integer part |
{x} | fractional part |
|x| | absolute value |
|z| | modulus |
z̄ | conjugate |
ℜz, Re z | real part |
ℑz, Im z | imaginary part |
directed line-segment | |
length | |
‖P‖ | norm |
√ | square root |
≠, <, ≤, >, ≥ | inequality |
≈ | approximation |
≡ | congruence |
∝ | proportion |
summation notation | |
product notation | |
π | pi |
f: x↦y | function, mapping |
ƒ: S → T | function, mapping |
→ | limit |
↗, ↘ | limit from the left and right |
ƒ ◯ g | composition |
ƒ^{−1} | inverse function, inverse mapping |
derivative, derived function | |
higher derivative | |
higher derivative | |
partial derivative | |
ƒ_{xx}, ƒ_{xy},…, ƒ_{11}, ƒ_{12},… | higher-order partial derivative |
higher-order partial derivative | |
ẋ, ẍ | rate of change |
∫ | integral, antiderivative |
a.b | scalar product |
a×b, a ∧ b | vector product |
a.(b×c), [a, b, c] | scalar triple product |
a×(b×c) | vector triple product |
A^{T}, A^{t}, A′ | transpose |
A^{−1} | inverse matrix |
|A| | determinant |
〈G, ◯〉 | group |
〈R,+,×〉 | ring |
E(X) | expected value |
Var(X) | variance |
Cov(X, Y) | covariance |
Pr(A) | probability |
Pr(A|B) | conditional probability |