# Symbols:E

### Identity Element

- $e$

Denotes the identity element in a general algebraic structure.

If $e$ is the identity of the structure $\struct {S, \circ}$, then a subscript is often used: $e_S$.

This is particularly common when more than one structure is under discussion.

The $\LaTeX$ code for \(e_S\) is `e_S`

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### Euler's Number

- $e$

Euler's number $e$ is the base of the natural logarithm $\ln$.

$e$ is defined to be the unique real number such that the value of the (real) exponential function $e^x$ has the same value as the slope of the tangent line to the graph of the function.

The $\LaTeX$ code for \(e\) is `e`

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### Eccentricity

- $e$

Used to denote the eccentricity of a conic section.

The $\LaTeX$ code for \(e\) is `e`

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### exa-

- $\mathrm E$

The Système Internationale d'Unités symbol for the metric scaling prefix **exa**, denoting $10^{\, 18 }$, is $\mathrm { E }$.

Its $\LaTeX$ code is `\mathrm {E}`

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### Hexadecimal

- $\mathrm E$ or $\mathrm e$

The hexadecimal digit $14$.

Its $\LaTeX$ code is `\mathrm E`

or `\mathrm e`

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### Duodecimal

- $\mathrm E$

The duodecimal digit $11$.

Its $\LaTeX$ code is `\mathrm E`

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### Set

- $E$

Used by some authors to denote a general set.

The $\LaTeX$ code for \(E\) is `E`

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### Complete Elliptic Integral of the Second Kind

- $\map E k$

- $\ds \map E k = \int \limits_0^{\pi / 2} \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$

is the **complete elliptic integral of the second kind**, and is a function of $k$, defined on the interval $0 < k < 1$.

The $\LaTeX$ code for \(\map E k\) is `\map E k`

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### Experiment

- $\mathcal E$

An **experiment**, which can conveniently be denoted $\EE$, is a probability space $\struct {\Omega, \Sigma, \Pr}$.

The $\LaTeX$ code for \(\mathcal E\) is `\mathcal E`

or `\EE`

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### Expectation

- $\expect X$

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a real-valued discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.

The **expectation of $X$**, written $\expect X$, is defined as:

- $\expect X := \ds \sum_{x \mathop \in \image X} x \map \Pr {X = x}$

whenever the sum is absolutely convergent, that is, when:

- $\ds \sum_{x \mathop \in \image X} \size {x \map \Pr {X = x} } < \infty$

The $\LaTeX$ code for \(\expect X\) is `\expect X`

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### Conditional Expectation

- $\expect {X \mid B}$

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

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

Let $B$ be an event in $\struct {\Omega, \Sigma, \Pr}$ such that $\map \Pr B > 0$.

The **conditional expectation of $X$ given $B$** is written $\expect {X \mid B}$ and defined as:

- $\expect {X \mid B} = \ds \sum_{x \mathop \in \image X} x \condprob {X = x} B$

where:

- $\condprob {X = x} B$ denotes the conditional probability that $X = x$ given $B$

whenever this sum converges absolutely.

The $\LaTeX$ code for \(\expect {X \mid B}\) is `\expect {X \mid B}`

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### East

- $\mathrm E$

### East (Terrestrial)

**East** is the direction on (or near) Earth's surface along the small circle in the direction of Earth's rotation in space about its axis.

### East (Celestial)

The $\LaTeX$ code for \(\mathrm E\) is `\mathrm E`

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### Energy

- $E$

The usual symbol used to denote the **energy** of a body is $E$.

Its $\LaTeX$ code is `E`

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### Electric Field Strength

- $\mathbf E$

The usual symbol used to denote **electric field strength** is $\mathbf E$.

Its $\LaTeX$ code is `\mathbf E`

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### Electromotive Force

- $\EE$

The usual symbol used to denote **electromotive force** is $\EE$.

Its $\LaTeX$ code is `\EE`

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### Elementary Charge

- $\E$

The symbol used to denote the **elementary charge** is usually $\E$ or $e$.

The preferred symbol on $\mathsf{Pr} \infty \mathsf{fWiki}$ is $\E$.

Its $\LaTeX$ code is `\E`

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