# Symbols:T

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### Time

$t$

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

The $\LaTeX$ code for $t$ is t .

### Independent Parameter

$t$

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

The $\LaTeX$ code for $t$ is t .

### 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} .

### 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 .

### 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 .

### 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} .

### 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 .

### 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 .

### 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 .

The $\LaTeX$ code for $T_{2 \frac 1 2}$ is T_{2 \frac 1 2} .

### 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 .

### 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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