# Symbols:T

### Time

- $t$

The usual symbol used to denote **time** is $t$.

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

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### Independent Parameter

- $t$

Often used to denote the independent parameter in a set of parametric equations.

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

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### Hour Angle

- $t$

Used to denote the **hour angle** of a point on the celestial sphere.

Let $P$ be a point on the celestial sphere.

The **hour angle** of $P$ is the angular distance measured westwards along the celestial equator from the vernal equinox.

That is, it is the angular distance measured westwards along the celestial equator between the observer's meridian and the hour circle of $P$.

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

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### tera-

- $\mathrm T$

The Système Internationale d'Unités symbol for the metric scaling prefix **tera**, denoting $10^{\, 12 }$, is $\mathrm { T }$.

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

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### Duodecimal

- $\mathrm T$

The duodecimal digit $10$.

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

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### Set

- $T$

Used to denote a general set, often in conjunction with $S$ when two such sets are under discussion.

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

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### tanh

- $\tanh$

The **hyperbolic tangent** function.

Its $\LaTeX$ code is `\tanh`

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### Inverse Tangent

- $\tan^{-1}$

Its $\LaTeX$ code is `\tan^{-1}`

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### Inverse Hyperbolic Tangent

#### tanh${}^{-1}$

- $\tanh^{-1}$

Its $\LaTeX$ code is `\tanh^{-1}`

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#### th${}^{-1}$

- $\operatorname {th}^{-1}$

A variant of **$\tanh^{-1}$**.

Its $\LaTeX$ code is `\operatorname {th}^{-1}`

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### Kinetic Energy

- $T$

The symbol used to denote **kinetic energy** is often $T$.

Its $\LaTeX$ code is `T`

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### Period of Oscillation

- $T$

The symbol used to denote **period of oscillation** is often $T$.

Its $\LaTeX$ code is `T`

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### Tesla

- $\mathrm T$

The symbol for the **tesla** is $\mathrm T$.

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

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### True

- $\T$

Symbol generally used for **truth**.

A statement has a truth value of **true** if and only if what it says matches the way that things are.

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

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### Algebraic Substructure

- $T$

Used to denote a general algebraic substructure of the algebraic structure $S$, in particular a subsemigroup.

In this context, frequently seen in the compound symbol $\struct {T, \circ}$ where $\circ$ represents an arbitrary binary operation.

The $\LaTeX$ code for \(\struct {T, \circ}\) is `\struct {T, \circ}`

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### Topological Space

- $T = \struct {S, \tau}$

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

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

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### Binary Operation

- $\intercal$

Used in 1975: T.S. Blyth: *Set Theory and Abstract Algebra* to denote an arbitrary binary operation in a general algebraic structure.

It is given the name **truc**, pronounced **trook**, French for **trick** or **technique**.

Blyth himself suggests that **truc** could be translated as **thingummyjig**, but this is linguistically unsupported, and is probably idiosyncratic.

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

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### Tychonoff Separation Axioms

- $T_0$, $T_1$, $T_2$, $T_{2 \frac 1 2}$, and so on

Symbol used for **Tychonoff Separation Axioms**.

The **Tychonoff separation axioms** are a classification system for topological spaces.

They are not axiomatic as such, but they are conditions that may or may not apply to general or specific topological spaces.

The $\LaTeX$ code for \(T_0\) is `T_0`

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The $\LaTeX$ code for \(T_{2 \frac 1 2}\) is `T_{2 \frac 1 2}`

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### Student's $t$-Distribution

- $\StudentT k$

Symbol used for **Student's $t$-Distribution**.

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

Let $\Img X = \R$.

$X$ is said to have a **Student's $t$-distribution with $k$ degrees of freedom** if and only if it has probability density function:

- $\map {f_X} x = \dfrac {\map \Gamma {\frac {k + 1} 2} } {\sqrt {\pi k} \map \Gamma {\frac k 2} } \paren {1 + \dfrac {x^2} k}^{-\frac {k + 1} 2}$

for some $k \in \R_{>0}$.

This is written:

- $X \sim \StudentT k$

The $\LaTeX$ code for \(X \sim \StudentT k\) is `X \sim \StudentT k`

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### Transpose of Matrix

- $\mathbf A^\intercal$

Symbol used for **Transpose of Matrix**.

Let $\mathbf A = \sqbrk \alpha_{m n}$ be an $m \times n$ matrix over a set.

Then the **transpose** of $\mathbf A$ is denoted $\mathbf A^\intercal$ and is defined as:

- $\mathbf A^\intercal = \sqbrk \beta_{n m}: \forall i \in \closedint 1 n, j \in \closedint 1 m: \beta_{i j} = \alpha_{j i}$

The $\LaTeX$ code for \(\mathbf A^\intercal\) is `\mathbf A^\intercal`

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### Tonne

- $\mathrm t$

The symbol for the **tonne** is $\mathrm t$.

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

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### Ton Force

- $\mathrm {tonf}$

The symbol for the **ton force** is $\mathrm {tonf}$.

The $\LaTeX$ code for \(\mathrm {tonf}\) is `\mathrm {tonf}`

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### Ton per Square Inch

- $\mathrm {tonf / in^2}$

The symbol for the **ton per square inch** is $\mathrm {tonf / in^2}$.

The $\LaTeX$ code for \(\mathrm {tonf / in^2}\) is `\mathrm {tonf / in^2}`

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### Ton-Foot

- $\mathrm {tonf \cdot ft}$

The symbol for the **ton-foot** is $\mathrm {tonf \cdot ft}$.

Its $\LaTeX$ code is `\mathrm {tonf \cdot ft}`

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### Ton-Foot: Variant

- $\mathrm {tonf \, ft}$

The symbol for the **ton-foot** can also be presented as $\mathrm {tonf \, ft}$.

Its $\LaTeX$ code is `\mathrm {tonf \, ft}`

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### Torr

- $\mathrm {Torr}$

The symbol for the **torr** is $\mathrm {Torr}$.

The $\LaTeX$ code for \(\mathrm {Torr}\) is `\mathrm {Torr}`

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