Symbols:Greek

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Alpha

The $1$st letter of the Greek alphabet.

Minuscule: $\alpha$
Majuscule: $\Alpha$

The $\LaTeX$ code for \(\alpha\) is \alpha .

The $\LaTeX$ code for \(\Alpha\) is \Alpha .


Beta

The $2$nd letter of the Greek alphabet.

Minuscule: $\beta$
Majuscule: $\Beta$

The $\LaTeX$ code for \(\beta\) is \beta .

The $\LaTeX$ code for \(\Beta\) is \Beta .


Beta Function

The Beta Function $\Beta: \C \times \C \to \C$ is defined for $\operatorname{Re} \left({x}\right), \operatorname{Re} \left({y}\right) > 0$ as:

$\displaystyle \Beta \left({x, y}\right) := \int_{\mathop \to 0}^{\mathop \to 1} t^{x - 1} \left({1 - t}\right)^{y - 1} \rd t$


The $\LaTeX$ code for \(\Beta \left({x, y}\right)\) is \Beta \left({x, y}\right) .


Gamma

The $3$rd letter of the Greek alphabet.

Minuscule: $\gamma$
Majuscule: $\Gamma$

The $\LaTeX$ code for \(\gamma\) is \gamma .

The $\LaTeX$ code for \(\Gamma\) is \Gamma .


Gamma Function

$\Gamma \left({z}\right)$


Integral Form

The Gamma function $\Gamma: \C \to \C$ is defined, for the open right half-plane, as:

$\displaystyle \map \Gamma z = \map {\mathcal M \set {e^{-t} } } z = \int_0^{\to \infty} t^{z - 1} e^{-t} \rd t$

where $\mathcal M$ is the Mellin transform.


For all other values of $z$ except the non-positive integers, $\map \Gamma z$ is defined as:

$\map \Gamma {z + 1} = z \, \map \Gamma z$


Weierstrass Form

The Weierstrass form of the Gamma function is:

$\displaystyle \frac 1 {\Gamma \left({z}\right)} = z e^{\gamma z} \prod_{n \mathop = 1}^\infty \left({\left({1 + \frac z n}\right) e^{-z / n} }\right)$

where $\gamma$ is the Euler-Mascheroni constant.


The Weierstrass form is valid for all $\C$.


Hankel Form

The Hankel form of the Gamma function is:

$\displaystyle \frac 1 {\Gamma \left({z}\right)} = \dfrac 1 {2 \pi i} \oint_{\mathcal H} \frac {e^t \, \mathrm d t} {t^z}$

where $\mathcal H$ is the contour starting at $-\infty$, circling the origin in an anticlockwise direction, and returning to $-\infty$.


The Hankel form is valid for all $\C$.


Euler Form

The Euler form of the Gamma function is:

$\displaystyle \Gamma \left({z}\right) = \frac 1 z \prod_{n \mathop = 1}^\infty \left({\left({1 + \frac 1 n}\right)^z \left({1 + \frac z n}\right)^{-1}}\right) = \lim_{m \mathop \to \infty} \frac {m^z m!} {z \left({z + 1}\right) \left({z + 2}\right) \cdots \left({z + m}\right)}$

which is valid except for $z \in \left\{{0, -1, -2, \ldots}\right\}$.


The $\LaTeX$ code for \(\Gamma \left({z}\right)\) is \Gamma \left({z}\right) .


The Euler-Mascheroni Constant

$\gamma$


The Euler-Mascheroni Constant $\gamma$ is the real number that is defined as:

\(\displaystyle \gamma\) \(:=\) \(\displaystyle \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}\) $\quad$ $\quad$
\(\displaystyle \) \(=\) \(\displaystyle \lim_{n \mathop \to +\infty} \paren {H_n - \ln n}\) $\quad$ $\quad$

where $H_n$ is the harmonic series and $\ln$ is the natural logarithm.


Delta

The $4$th letter of the Greek alphabet.

Minuscule: $\delta$
Majuscule: $\Delta$

The $\LaTeX$ code for \(\delta\) is \delta .

The $\LaTeX$ code for \(\Delta\) is \Delta .


Diagonal Relation

$\Delta_S$


Let $S$ be a set.

The diagonal relation on $S$ is a relation $\Delta_S$ on $S$ such that:

$\Delta_S = \set {\tuple {x, x}: x \in S} \subseteq S \times S$

Alternatively:

$\Delta_S = \set {\tuple {x, y}: x, y \in S: x = y}$


The $\LaTeX$ code for \(\Delta_S\) is \Delta_S .


Product of Differences

$\Delta_n \left({x_1, x_2, \ldots, x_n}\right)$


Let $n \in \Z_{> 0}$ be a strictly positive integer.

Let $\tuple {x_1, x_2, \ldots, x_n}$ be an ordered $n$-tuple of real numbers.


The product of differences of $\tuple {x_1, x_2, \ldots, x_n}$ is defined and denoted as:

$\map {\Delta_n} {x_1, x_2, \ldots, x_n} = \displaystyle \prod_{1 \mathop \le i \mathop < j \mathop \le n} \paren {x_i - x_j}$


When the underlying ordered $n$-tuple is understood, the notation is often abbreviated to $\Delta_n$.


Thus $\Delta_n$ is the product of the difference of all ordered pairs of $\tuple {x_1, x_2, \ldots, x_n}$ where the index of the first is less than the index of the second.


The $\LaTeX$ code for \(\Delta_n \left({x_1, x_2, \ldots, x_n}\right)\) is \Delta_n \left({x_1, x_2, \ldots, x_n}\right) .


Kronecker Delta

$\delta_{x y}$


Let $\Gamma$ be a set.

Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.


Then $\delta_{\alpha \beta}: \Gamma \times \Gamma \to R$ is the mapping on the cartesian square of $\Gamma$ defined as:

$\forall \left({\alpha, \beta}\right) \in \Gamma \times \Gamma: \delta_{\alpha \beta} := \begin{cases} 1_R & :\alpha = \beta \\ 0_R & :\alpha \ne \beta \end{cases}$

This use of $\delta$ is known as the Kronecker delta notation or Kronecker delta convention.


It can be expressed in Iverson bracket notation as:

$\delta_{\alpha \beta} := \left[{\alpha = \beta}\right]$


The $\LaTeX$ code for \(\delta_{x y}\) is \delta_{x y} .


Change

$\Delta x_n$


$\Delta$ is often used to mean change or difference.

For example, for the definition of slope:

$\dfrac {\Delta y} {\Delta x} = \dfrac {y_2 - y_1} {x_2 - x_1} = \dfrac {\text{change in } y} {\text{change in } x}$


The $\LaTeX$ code for \(\Delta x_n\) is \Delta x_n .


Epsilon

The $5$th letter of the Greek alphabet.

Minuscules: $\epsilon$ and $\varepsilon$
Majuscule: $\Epsilon$

The $\LaTeX$ code for \(\epsilon\) is \epsilon .
The $\LaTeX$ code for \(\varepsilon\) is \varepsilon .

The $\LaTeX$ code for \(\Epsilon\) is \Epsilon .


Element of a Set

The notation for an object being an element of a set uses a stylized form of the letter $\epsilon$:

$x \in S$, $S \owns x$

This notation was invented by Peano, from the first letter of the Greek word είναι, meaning is.

The $\LaTeX$ code for \(\in\) is \in .

The $\LaTeX$ code for \(\owns\) is \owns  or \ni.


A small positive quantity

Many a proof in analysis will famously start:

"Let $\epsilon > 0$ ..."

where it is frequently left unstated that $\epsilon$ is a real number, arbitrarily small.

The $\LaTeX$ code for \(\epsilon > 0\) is \epsilon > 0 .


Zeta

The $6$th letter of the Greek alphabet.

Minuscule: $\zeta$
Majuscule: $\Zeta$

The $\LaTeX$ code for \(\zeta\) is \zeta .

The $\LaTeX$ code for \(\Zeta\) is \Zeta .


Riemann Zeta Function

$\zeta \left({s}\right)$


The Riemann Zeta Function $\zeta$ is the complex function defined on the half-plane $\map \Re s > 1$ as the series:

$\displaystyle \map \zeta s = \sum_{n \mathop = 1}^\infty \frac 1 {n^s}$


The $\LaTeX$ code for \(\zeta \left({s}\right)\) is \zeta \left({s}\right) .


Eta

The $7$th letter of the Greek alphabet.

Minuscule: $\eta$
Majuscule: $\Eta$

The $\LaTeX$ code for \(\eta\) is \eta .

The $\LaTeX$ code for \(\Eta\) is \Eta .


Theta

The $8$th letter of the Greek alphabet.

Minuscules: $\theta$ and $\vartheta$
Majuscule: $\Theta$

The $\LaTeX$ code for \(\theta\) is \theta .
The $\LaTeX$ code for \(\vartheta\) is \vartheta .

The $\LaTeX$ code for \(\Theta\) is \Theta .


Iota

The $9$th letter of the Greek alphabet.

Minuscule: $\iota$
Majuscule: $\Iota$

The $\LaTeX$ code for \(\iota\) is \iota .

The $\LaTeX$ code for \(\Iota\) is \Iota .

It is pronounced yot-ta, not the incorrect but often-heard eye-oh-ta.


Inclusion Mapping

Used by some sources to denote the mapping on $S$ to $T$ where $S \subseteq T$:

$\iota_S: S \to T: \forall x \in S: \iota_S \left({x}\right) = x$

The $\LaTeX$ code for \(\iota_S\) is \iota_S .


Identity Arithmetic Function

The identity arithmetic function $\iota: S \to \Z$ is defined for $n \geq 1$ by:

$\forall n \in S: \iota \left({n}\right) = \delta_{n1}$

where:

$S$ is (in theory) any set, but in this context is usually one of the standard number sets $\Z, \Q, \R, \C$.
$\delta$ is the Kronecker delta.


That is:

$\forall n \in S: \iota \left({n}\right) = \begin{cases} 1 & : n = 1\\ 0 & : n \ne 1 \end{cases}$


The $\LaTeX$ code for \(\iota \left({n}\right)\) is \iota \left({n}\right) .


Kappa

The $10$th letter of the Greek alphabet.

Minuscule: $\kappa$
Majuscule: $\Kappa$

The $\LaTeX$ code for \(\kappa\) is \kappa .

The $\LaTeX$ code for \(\Kappa\) is \Kappa .


Kernel

Used in abstract algebra and other related fields to denote the general kernel of a homomorphism.


Curvature

Let $C$ be a curve defined by a real function which is twice differentiable.


The curvature of a $C$ is the reciprocal of the radius of the osculating circle to $C$ and is often denoted $\kappa$ (Greek kappa).


Lambda

The $11$th letter of the Greek alphabet.

Minuscule: $\lambda$
Majuscule: $\Lambda$

The $\LaTeX$ code for \(\lambda\) is \lambda .

The $\LaTeX$ code for \(\Lambda\) is \Lambda .


Von Mangoldt Function

$\Lambda \left({n}\right)$


The von Mangoldt function $\Lambda: \N \to \R$ is defined as:

$\Lambda \left({n}\right) = \begin{cases} \ln \left({p}\right) & : \exists m \in \N, p \in \mathbb P: n = p^m \\ 0 & : \text{otherwise} \end{cases}$

where $\mathbb P$ is the set of all prime numbers.


The $\LaTeX$ code for \(\Lambda \left({n}\right)\) is \Lambda \left({n}\right) .


Linear Density

$\lambda$

Used to denote the linear density of a given one-dimensional body:

$\displaystyle \lambda = \frac m l$

where:


Parameter of Poisson Distribution

$\lambda$

Used to denote the parameter of a given Poisson distribution:


Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.


Then $X$ has the Poisson distribution with parameter $\lambda$ (where $\lambda > 0$) if:

$\Img X = \set {0, 1, 2, \ldots} = \N$
$\map \Pr {X = k} = \dfrac 1 {k!} \lambda^k e^{-\lambda}$


Left Regular Representation

$\lambda_a$

Let $\left ({S, \circ}\right)$ be an algebraic structure.


The mapping $\lambda_a: S \to S$ is defined as:

$\forall a \in S: \map {\lambda_a} x = a \circ x$


This is known as the left regular representation of $\struct {S, \circ}$ with respect to $a$.


The $\LaTeX$ code for \(\lambda_a\) is \lambda_a .


Mu

The $12$th letter of the Greek alphabet.

Minuscule: $\mu$
Majuscule: $\Mu$

The $\LaTeX$ code for \(\mu\) is \mu .

The $\LaTeX$ code for \(\Mu\) is \Mu .


micro-

$\mathrm \mu$

The Système Internationale d'Unités metric scaling prefix denoting $10^{\, -6 }$.


Its $\LaTeX$ code is \mathrm {\mu} .

Sources


Expectation

$\mu$

Often used to denote the expectation of a given random variable.


Linear Density

$\mu$

Used to denote the linear density of a given one-dimensional body:

$\displaystyle \mu = \frac m l$

where:


Parameter of Poisson Distribution

$\mu$

Used as an alternative to $\lambda$ to denote the parameter of a given Poisson distribution.


Moment of Discrete Random Variable

$\mu'_n$


Let $X$ be a discrete random variable.

Then the $n$th moment of $X$ is denoted $\mu'_n$ and defined as:

$\mu'_n = \expect {X^n}$

where $\expect {\, \cdot \,}$ denotes the expectation function.


The $\LaTeX$ code for \(\mu'_n\) is \mu'_n .


Nu

The $13$th letter of the Greek alphabet.

Minuscule: $\nu$
Majuscule: $\Nu$

The $\LaTeX$ code for \(\nu\) is \nu .

The $\LaTeX$ code for \(\Nu\) is \Nu .


Xi

The $14$th letter of the Greek alphabet.

Minuscule: $\xi$
Majuscule: $\Xi$

The $\LaTeX$ code for \(\xi\) is \xi .

The $\LaTeX$ code for \(\Xi\) is \Xi .


Omicron

The $15$th letter of the Greek alphabet.

Minuscule: $\omicron$
Majuscule: $\textrm O$

The $\LaTeX$ code for \(\omicron\) is \omicron .

The $\LaTeX$ code for \(\textrm O\) is \textrm O .


Pi

The $16$th letter of the Greek alphabet.

Minuscules: $\pi$ and $\varpi$
Majuscule: $\Pi$

The $\LaTeX$ code for \(\pi\) is \pi .
The $\LaTeX$ code for \(\varpi\) is \varpi .

The $\LaTeX$ code for \(\Pi\) is \Pi .


Real Constant

The real number $\pi$ (pronounced pie) is an irrational number (see proof here) whose value is approximately $3.14159\ 26535\ 89793\ 23846\ 2643 \ldots$


Prime-Counting Function

The prime-counting function is the function $\pi: \R \to \Z$ which counts the number of primes less than or equal to some real number.


That is:

$\displaystyle \forall x \in \R: \pi \left({x}\right) = \sum_{\substack {p \mathop \in \mathbb P \\ p \mathop \le x} } 1$


The $\LaTeX$ code for \(\pi \left({x}\right)\) is \pi \left({x}\right) .


Projection

The notation $\pi_i$ is often used for the $i$th projection.

The $\LaTeX$ code for \(\pi_i\) is \pi_i .


Probability Generating Function

$\Pi_X \left({s}\right)$


Let $X$ be a discrete random variable whose codomain, $\Omega_X$, is a subset of the natural numbers $\N$.

Let $p_X$ be the probability mass function for $X$.


The probability generating function for $X$, denoted $\Pi_X \left({s}\right)$, is the formal power series defined by:

$\displaystyle \Pi_X \left({s}\right) := \sum_{n \mathop = 0}^\infty p_X \left({n}\right) s^n \in \R \left[\left[{s}\right]\right]$


The $\LaTeX$ code for \(\Pi_X \left({s}\right)\) is \Pi_X \left({s}\right) .


Product Notation

Let $\left({S, \times}\right)$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.


The composite is called the product of $\left({a_1, a_2, \ldots, a_n}\right)$, and is written:

$\displaystyle \prod_{j \mathop = 1}^n a_j = \left({a_1 \times a_2 \times \cdots \times a_n}\right)$


The $\LaTeX$ code for \(\displaystyle \prod_{j \mathop = 1}^n a_j\) is \displaystyle \prod_{j \mathop = 1}^n a_j .

The $\LaTeX$ code for \(\displaystyle \prod_{1 \mathop \le j \mathop \le n} a_j\) is \displaystyle \prod_{1 \mathop \le j \mathop \le n} a_j .

The $\LaTeX$ code for \(\displaystyle \prod_{\Phi \left({j}\right)} a_j\) is \displaystyle \prod_{\Phi \left({j}\right)} a_j .


Rho

The $17$th letter of the Greek alphabet.

Minuscules: $\rho$ and $\varrho$
Majuscule: $\Rho$

The $\LaTeX$ code for \(\rho\) is \rho .
The $\LaTeX$ code for \(\varrho\) is \varrho .

The $\LaTeX$ code for \(\Rho\) is \Rho .


Density

$\rho$


Used to denote the density of a given body:

$\rho = \dfrac m V$

where:


Area Density

$\rho_A$


Used to denote the area density of a given two-dimensional body:

$\rho_A = \dfrac m A$

where:

  • $m$ is the body's mass;
  • $A$ is the body's area.


The $\LaTeX$ code for \(\rho_A\) is \rho_A .


Right Regular Representation

$\rho_a$

Let $\left ({S, \circ}\right)$ be an algebraic structure.


The mapping $\rho_a: S \to S$ is defined as:

$\forall a \in S: \map {\rho_a} x = x \circ a$


This is known as the right regular representation of $\struct {S, \circ}$ with respect to $a$.


The $\LaTeX$ code for \(\rho_a\) is \rho_a .


Radius of Curvature

The radius of curvature of a curve $C$ at a point $P$ is defined as the reciprocal of the absolute value of its curvature:

$\rho = \dfrac 1 {\left\lvert{k}\right\rvert}$



Sigma

The $18$th letter of the Greek alphabet.

Minuscules: $\sigma$ and $\varsigma$
Majuscule: $\Sigma$

The $\LaTeX$ code for \(\sigma\) is \sigma .
The $\LaTeX$ code for \(\varsigma\) is \varsigma .

The $\LaTeX$ code for \(\Sigma\) is \Sigma .


Event Space

$\Sigma$


Let $\mathcal E$ be an experiment.


The event space of $\mathcal E$ is usually denoted $\Sigma$ (Greek capital sigma), and is the set of all outcomes of $\mathcal E$ which are interesting.


Summation

Let $\left({S, +}\right)$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.


The composite is called the summation of $\left({a_1, a_2, \ldots, a_n}\right)$, and is written:

$\displaystyle \sum_{j \mathop = 1}^n a_j = \left({a_1 + a_2 + \cdots + a_n}\right)$


The $\LaTeX$ code for \(\displaystyle \sum_{j \mathop = 1}^n a_j\) is \displaystyle \sum_{j \mathop = 1}^n a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j\) is \displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{\Phi \left({j}\right)} a_j\) is \displaystyle \sum_{\Phi \left({j}\right)} a_j .


Sigma Function

$\sigma \left({n}\right)$


Let $n$ be an integer such that $n \ge 1$.

The sigma function $\map \sigma n$ is defined on $n$ as being the sum of all the positive integer divisors of $n$.

That is:

$\displaystyle \map \sigma n = \sum_{d \mathop \divides n} d$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.


The $\LaTeX$ code for \(\sigma \left({n}\right)\) is \sigma \left({n}\right) .


Surface Charge Density

$\sigma$

Used to denote the surface charge density of a given body:

$\displaystyle \sigma = \frac q A$

where:


Area Density

$\sigma$

Used sometimes, although $\rho_A$ (Greek letter rho) is more common, to denote the area density of a given two-dimensional body:

$\sigma = \dfrac m A$

where:

  • $m$ is the body's mass;
  • $A$ is the body's area.


Tau

The $19$th letter of the Greek alphabet.

Minuscule: $\tau$
Majuscule: $\Tau$

The $\LaTeX$ code for \(\tau\) is \tau .

The $\LaTeX$ code for \(\Tau\) is \Tau .


Tau Function

$\tau \left({n}\right)$


Let $n$ be an integer such that $n \ge 1$.

The $\tau$ (tau) function is defined on $n$ as being the total number of positive integer divisors of $n$.

That is:

$\displaystyle \map \tau n = \sum_{d \mathop \divides n} 1$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.


The $\LaTeX$ code for \(\tau \left({n}\right)\) is \tau \left({n}\right) .


Topology

$\tau$

Frequently used, and conventionally in many texts, to denote a general topology.

It is usually introduced as part of the notation $T = \left({S, \tau}\right)$ for a general topological space.


The $\LaTeX$ code for \(\tau\) is \tau .


Upsilon

The $20$th letter of the Greek alphabet.

Minuscule: $\upsilon$
Majuscule: $\Upsilon$

The $\LaTeX$ code for \(\upsilon\) is \upsilon .

The $\LaTeX$ code for \(\Upsilon\) is \Upsilon .


Phi

The $21$st letter of the Greek alphabet.

Minuscules: $\phi$ and $\varphi$
Majuscules: $\Phi$ and $\varPhi$

The $\LaTeX$ code for \(\phi\) is \phi .
The $\LaTeX$ code for \(\varphi\) is \varphi .

The $\LaTeX$ code for \(\Phi\) is \Phi .
The $\LaTeX$ code for \(\varPhi\) is \varPhi .


Euler Phi Function

$\phi \left({n}\right)$


Let $n \in \Z_{>0}$, that is, a strictly positive integer.


The Euler $\phi$ (phi) function is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:

$\phi \left({n}\right) = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$


That is:

$\phi \left({n}\right) = \left|{S_n}\right|: S_n = \left\{{k: 1 \le k \le n, k \perp n}\right\}$


The $\LaTeX$ code for \(\phi \left({n}\right)\) is \phi \left({n}\right) .


Golden Mean

$\phi$


Let a line segment $AB$ be divided at $C$ such that:

$AB : AC = AC : BC$

Then the golden mean $\phi$ is defined as:

$\phi := \dfrac {AB} {AC}$


The $\LaTeX$ code for \(\phi\) is \phi .


Mapping

$\phi \left({x}\right)$

The Greek letter $\phi$, along with $\psi$ and $\chi$ and others, is often used to denote a general mapping.

In the context of abstract algebra, it often denotes a homomorphism.


The $\LaTeX$ code for \(\phi \left({x}\right)\) is \phi \left({x}\right) .


Chi

The $22$nd letter of the Greek alphabet.

Minuscule: $\chi$
Majuscule: $\Chi$

The $\LaTeX$ code for \(\chi\) is \chi .

The $\LaTeX$ code for \(\Chi\) is \Chi .


Mapping

$\chi \left({x}\right)$

The Greek letter $\chi$, along with $\psi$ and $\phi$ and others, is often used to denote a general mapping.

In the context of abstract algebra, it often denotes a homomorphism.


The $\LaTeX$ code for \(\chi \left({x}\right)\) is \chi \left({x}\right) .


Characteristic Function

$\chi_E$


Let $E \subseteq S$.

The characteristic function of $E$ is the function $\chi_E: S \to \left\{{0, 1}\right\}$ defined as:

$\chi_E \left({x}\right) = \begin{cases} 1 & : x \in E \\ 0 & : x \notin E \end{cases}$

That is:

$\chi_E \left({x}\right) = \begin{cases} 1 & : x \in E \\ 0 & : x \in \complement_S \left({E}\right) \end{cases}$

where $\complement_S \left({E}\right)$ denotes the complement of $E$ relative to $S$.


The $\LaTeX$ code for \(\chi_E\) is \chi_E .


Psi

The $23$rd letter of the Greek alphabet.

Minuscule: $\psi$
Majuscule: $\Psi$

The $\LaTeX$ code for \(\psi\) is \psi .

The $\LaTeX$ code for \(\Psi\) is \Psi .


Mapping

$\psi \left({x}\right)$

The Greek letter $\psi$, along with $\phi$ and $\chi$ and others, is often used to denote a general mapping.

In the context of abstract algebra, it often denotes a homomorphism.


The $\LaTeX$ code for \(\psi \left({x}\right)\) is \psi \left({x}\right) .


Omega

The $24$th and final letter of the Greek alphabet.

Minuscule: $\omega$
Majuscule: $\Omega$

The $\LaTeX$ code for \(\omega\) is \omega .

The $\LaTeX$ code for \(\Omega\) is \Omega .


Sample Space

$\Omega$


Let $\mathcal E$ be an experiment.


The sample space of $\mathcal E$ is usually denoted $\Omega$ (Greek capital omega), and is defined as the set of all possible outcomes of $\mathcal E$.


Elementary Event

$\omega$


Let $\mathcal E$ be an experiment.


An elementary event of $\mathcal E$, often denoted $\omega$ (Greek lowercase omega) is one of the elements of the sample space $\Omega$ (Greek capital omega) of $\mathcal E$.


Order Type of Natural Numbers

$\omega$


The order type of $\left({\N, \le}\right)$ is denoted $\omega$ (omega).


Relation

$\omega$

Used in some sources, for example 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.), to denote a general relation.


Greek Alphabet

Position Lowercase Uppercase Name
1 $\alpha$ $\Alpha$ Alpha
2 $\beta$ $\Beta$ Beta
3 $\gamma$ $\Gamma$ Gamma
4 $\delta$ $\Delta$ Delta
5 $\epsilon$ $\Epsilon$ Epsilon
6 $\zeta$ $\Zeta$ Zeta
7 $\eta$ $\Eta$ Eta
8 $\theta$ $\Theta$ Theta
9 $\iota$ $\Iota$ Iota
10 $\kappa$ $\Kappa$ Kappa
11 $\lambda$ $\Lambda$ Lambda
12 $\mu$ $\Mu$ Mu
13 $\nu$ $\Nu$ Nu
14 $\xi$ $\Xi$ Xi
15 $o$ $\textrm O$ Omicron
16 $\pi$ $\Pi$ Pi
17 $\rho$ $\Rho$ Rho
18 $\sigma$ $\Sigma$ Sigma
19 $\tau$ $\Tau$ Tau
20 $\upsilon$ $\Upsilon$ Upsilon
21 $\phi$ $\Phi$ Phi
22 $\chi$ $\Chi$ Chi
23 $\psi$ $\Psi$ Psi
24 $\omega$ $\Omega$ Omega
Lowercase variants
25 $\varepsilon$ Varepsilon
26 $\vartheta$ Vartheta
27 $\varpi$ Varpi
28 $\varrho$ Varrho
29 $\varsigma$ Varsigma
30 $\varphi$ Varphi