# Symbols:T

### Time

- $t$

Used in applied mathematics to denote time when used as an independent variable.

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

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### Independent Parameter

- $t$

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

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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### 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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### 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 **$t$-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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