Symbols & Notations

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Page last updated: 20.10.2016

Symbol / Notation Meaning
= is equal to …
\neq is not equal to…
\equiv is identical or congruent to …
\approx is approximately equal to …
\cong is isomorphic to …
\propto is proportional to …
< is less than …
\le is less than or equal to …
\nless is not less than …
greater_than is greater than …
\ge is greater than or equal to …
\ngtr is not greater than …
x\wedge y x and y
x\vee y x or y (or both)
x\Rightarrow y x implies that y (if x then y)
x\Leftarrow y x is implied by y (if y then x)
x\Leftrightarrow y x implies and is implied by y (x is equivalent to y)
\sim x not x
\in is an element of …
\notin is not an element of …
\exists there exists …
\forall for all …
\infty infinity
\left\{ { x }_{ 1 },{ x }_{ 2 },{ x }_{ 3 },... \right\} a set with elements { x }_{ 1 },{ x }_{ 2 },{ x }_{ 3 },...\quad
\left\{ x:... \right\} the set of all x such that …
n\left( A \right) the number of elements in set A
\emptyset ,\{ \} an empty set
\xi the universal set
A the complement of the set A
\subseteq is a subset of …
\supseteq is a superset of …
\subset is a proper subset of …
\cup union
\cap intersection
\mathbb{N} the set of natural numbers, \left\{ 1,2,3,4,... \right\}
\mathbb{Z} the set of integers, \left\{ 0,\pm 1,\pm 2,\pm 3,... \right\}
\mathbb{Z}^+ the set of positive integers, \left\{ 1,2,3,4,... \right\}
\mathbb{Z}_n the set of integers modulo n, \left\{ 1,2,3,4,..,n-1 \right\}
\mathbb{Q} the set of rational numbers, \left\{ \frac { a }{ b } :a\in \mathbb{Z}_u,\quad b\in \mathbb{Z}^+ \right\}
\mathbb{Q}^+ the set of positive rational numbers, part_2
\mathbb{Q}_0^+ the set of positive rational numbers including zero, \{ x\in \mathbb{Q}:x\ge 0\}
\mathbb{R} the set of real numbers
\mathbb{R}^+ the set of positive real numbers, part_3
\mathbb{R}_0^+ the set of positive real numbers including zero, \{ x\in \mathbb{R}:x\ge 0\}
\mathbb{C} the set of complex numbers
[p,q] a closed interval, \left\{ x\in \mathbb{R}:p\le x\le q \right\}
[p,q), [p,q[ the interval, \left\{ x\in \mathbb{R}:p\le x<q \right\}
(p,q], ]p,q] the interval, \left\{ x\in \mathbb{R}:p<x\le q \right\}
(p,q), ]p,q[ an open interval, \left\{ x\in \mathbb{R}:p<x<q \right\}
summation_symbol { a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+...+{ a }_{ n }
multiplication symbol { a }_{ 1 }\times { a }_{ 2 }\times { a }_{ 3 }\times ...\times { a }_{ n }
\sqrt { n } the positive square root of n
\left| n \right| the modulus of n
n! 1\times 2\times 3\times ...\times \left( n-2 \right) \times \left( n-1 \right) \times n
\left( \begin{matrix} n \\ k \end{matrix} \right) n choose k
f\left( x \right) the function of x
{ f }^{ -1 } the inverse of the function
\Delta x,\quad \delta x change in x
\frac { dy }{ dx } the derivative of y with respect to x
\frac { { d }^{ n }y }{ d{ x }^{ n } } the nth derivative of y with respect to x
f the first, second, …, and nth derivatives of the function of x with respect to x
\int { ydx } y integrated
\int _{ a }^{ b }{ ydx } y integrated between the limits a and b
\frac { \partial A }{ \partial x } the partial derivative of A with respect to x
e base of natural logarithms, with a value of approximately 2.718
{ e }^{ x },exp\quad x exponential function of x
\log _{ a }{ x } logarithm of x to the base a
\ln { x } ,\log _{ e }{ x } the natural logarithm of x

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