Scripts, accents, fonts

Accents I will actually put on letters. If a hat becomes a floating combining mark, the Fourier transform is unreadable.

\hat{𝑓},\quad \tilde{𝑔},\quad \dot{𝑥},\quad \ddot{𝑦},\quad \vec{𝑣},\quad \check{𝑎}

(3.98)

A limit, a maximum, an infimum. Scripts on operators are not the same as scripts on letters.

\lim _{𝑥\to 0}\frac{\sin 𝑥}{𝑥}=1

(3.99)

\max _{1\leq 𝑖\leq 𝑛}{𝑎}_{𝑖}

(3.100)

\inf _{𝑥\in \mathbb{R}}𝑓(𝑥)

(3.101)

\sup _{𝑛\in \mathbb{N}}{𝑠}_{𝑛}

(3.102)

\limsup _{𝑛\to \infty }{𝑎}_{𝑛}

(3.103)

Sum and product with a condition in the subscript, not a dummy that starts at 1:

\sum _{𝑝\, \text{ prime}}\frac{1}{{𝑝}^{𝑠}}

(3.104)

\prod _{𝑘=1}^{𝑛}(1+{𝑥}_{𝑘})=\exp \sum _{𝑘=1}^{𝑛}\log (1+{𝑥}_{𝑘})

(3.105)

Nested fractions, four deep. A converter that only does one mfrac dies here.

1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5}}}}

(3.106)

A fraction of fractions:

\frac{\frac{𝑎}{𝑏}}{\frac{𝑐}{𝑑}}=\frac{𝑎𝑑}{𝑏𝑐}

(3.107)

Leibniz mixed with a higher-order ordinary derivative:

\frac{{\mathrm{d}}^{2}𝑦}{\mathrm{d}{𝑥}^{2}}+\frac{\mathrm{d}𝑦}{\mathrm{d}𝑥}+𝑦=0

(3.108)

\frac{{\partial }^{2}𝑢}{\partial 𝑥\partial 𝑦}

(3.109)

Overbrace and underbrace on the same identity, so both attachments exist:

\overset{\text{three}}{\overbrace{𝑎+𝑏+𝑐}}=\underbrace{𝑥+𝑦+𝑧}_{\text{also three}}

(3.110)

A question sitting over an equals, the attach I use when I have not justified a step:

\overset{?}{=}

(3.111)

A minimum sitting under an operator:

\min _{𝑥\in 𝐾}𝑓(𝑥)

(3.112)

Delimiters that have to stretch. Floor, ceiling, absolute value, a norm, an inner product, a closed interval.

\lfloor 𝑥\rfloor \leq 𝑥<\lceil 𝑥\rceil

(3.113)

|𝑥+𝑦|\leq |𝑥|+|𝑦|

(3.114)

\|𝐴𝑣\|\leq \|𝐴\|\|𝑣\|

(3.115)

\langle 𝑢,𝑣\rangle ={𝑢}_{1}{𝑣}_{1}+{𝑢}_{2}{𝑣}_{2}

(3.116)

[𝑎,𝑏]\subset \mathbb{R}

(3.117)

Set builder, quantifiers, empty set, unions:

\{𝑥\in \mathbb{R}:𝑥>0\}

(3.118)

\forall \varepsilon >0,\exists 𝑁\in \mathbb{N}

(3.119)

𝐴\cup 𝐵\cap 𝐶,\quad \emptyset \subseteq 𝐴

(3.120)

Maps and relations I type constantly:

𝑓:\mathbb{R}\to \mathbb{R},\quad 𝑥\mapsto {𝑥}^{2}

(3.121)

𝑎\equiv 𝑏\quad (\operatorname{mod}𝑛),\quad 𝑎\approx 𝑏,\quad 𝑎\simeq 𝑐

(3.122)

𝑎\oplus 𝑏,\quad 𝑢\otimes 𝑣,\quad 𝐴\sqcup 𝐵

(3.123)

𝐴\subset 𝐵\subseteq 𝐶,\quad 𝑥\in 𝐴,\quad 𝑥\notin 𝐵

(3.124)

Blackboard, calligraphic, fraktur, bold. If they all render as italic $𝑥$ , the fonts never loaded.

\mathbb{R},\mathbb{Z},\mathbb{N},\mathbb{Q},\mathbb{C},\quad \mathcal{L},\mathcal{F},\mathcal{H},\quad 𝔤,𝔥,\quad 𝒗,𝑨

(3.125)

Greek I will not pretend I can skip:

\alpha ,\beta ,\gamma ,\Gamma ,\delta ,\Delta ,\epsilon ,\zeta ,\eta ,\theta ,\vartheta ,\iota ,\kappa ,\lambda ,\Lambda ,\mu ,\nu ,\xi ,\Xi ,\pi ,\Pi ,\rho ,\sigma ,\Sigma ,\tau ,\phi ,\varphi ,\chi ,\psi ,\Psi ,\omega ,\Omega

(3.126)

Superscripts that are not exponents: transpose, inverse, adjoint, a parenthesized order of derivative.

{𝐴}^{𝑇},\quad {𝐴}^{-1},\quad {𝐴}^{\ast },\quad {𝑓}^{(𝑛)}(𝑥)

(3.127)

A double subscript and a stacked exponent:

{𝑎}_{𝑖𝑗}^{𝑛+1},\quad {𝑥}_{𝑖}^{(𝑘)},\quad {\Gamma }_{𝑖𝑗}^{𝑘}

(3.128)

Big-O and little-o next to a logarithm, because log is a function name, not three letters:

𝑓(𝑛)=𝑂(𝑛\log 𝑛)+𝑜(1)

(3.129)

Complex exponential, so $𝑒$ , $𝑖$ , and $\pi$ share a superscript:

{𝑒}^{𝑖\pi }+1=0

(3.130)

A binomial coefficient that is not a matrix, next to a multinomial written as a fraction:

\frac{𝑛!}{{𝑘}_{1!}{𝑘}_{2!}{𝑘}_{3!}}=\frac{𝑛!}{{𝑘}_{1!}{𝑘}_{2!}{𝑘}_{3!}}

(3.131)