# Symbols:Greek

## 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} .

### 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