Formatting Sandbox I: please **don't** test stuff here [duplicate]

Question

This thread has been retired due to the large number of posts. The newest sandbox can be found here:

Formatting Sandbox III: please test stuff here

Before that, there was also this Sandbox:

Formatting Sandbox II: please *don't* test stuff here

What the title says.

Use this for testing stuff instead of bumping random posts to the mainspace a million times.

Answer 1

$\textrm{UP UP AND AWA}^{ \textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{a}^{\textrm{a}^{\textrm{a}^{\textrm{a} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{y}^{\textrm{y}^{\textrm{y}^{\textrm{y} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} ^{\textrm{!}^{\textrm{!}^{\textrm{!}^{\textrm{!} }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}_{ \textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{a}_{\textrm{a}_{\textrm{a}_{\textrm{a} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{y}_{\textrm{y}_{\textrm{y}_{\textrm{y} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} _{\textrm{!}_{\textrm{!}_{\textrm{!}_{\textrm{!} }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

And now we know ^ and _ is supported to at least 140 levels.

Answer 2

How to make a table in LaTeX:

\begin{array}{|c|c|c|c|}\hline Alcolic \space beverage & Carboydrate \space content(\%) & pH \\ \hline Beer & 3.0-5.0 & 4.1-4.5 \\ \hline Wine & 0.0-12.9 & 2.8-3.8 \\ \hline Sweet \space liquor & 30.0-31.0 & 3.3-3.9 \\ \hline Strong \space alcohol & 0.0-1.2 & 6.5-6.9\\ \hline Vodka & very \space few & 6.0-7.0 \\ \hline Coca Cola & 10.6(?) & 2.8\\ \hline \end{array}

How to make the table look like it wasn't done in math mode (considerably more code, but nicer output) and also give it a slightly cleaner look: $$ \small \begin{array}{lcc} \hline \text{Beverage} & \text{Carbohydrate Content (%)} & \text{pH} \\ \hline \text{Beer} & 3.0-5.0 & 4.1-4.5 \\ \text{Wine} & 0.0-12.9 & 2.8-3.8 \\ \text{Sweet liquor } & 30.0-31.0 & 3.3-3.9 \\ \text{Strong alcohol} & 0.0-1.2 & 6.5-6.9 \\ \text{Vodka} & \text{very little} & 6.0-7.0 \\ \text{Coca Cola} & 10.6(?) & 2.8 \\ \hline \end{array} $$

Answer 3

Align at point:
Define for easier typsetting \newcommand{\d}[2]{#1.&\hspace{-1em}#2}
and use in table 1.23 as \d{1}{23}

$$\newcommand{\d}[2]{#1.&\hspace{-1em}#2} \begin{array}{lrl} \hline \text{Beverage} & \text{Nomnom}&\hspace{-1em}\text{-factor} \\ \hline \text{Beer} & 100.&\hspace{-1em}000 \\ \text{Wine} & 23.&\hspace{-1em}4567\\ \text{Cola stuff} & 1.&\hspace{-1em}23\\ \text{Coffee} & 66.&\hspace{-1em}6\\ \text{Tea (black)}&\d{0}{3}\\ \hline \end{array} $$

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The mhchem package is not enabled on StackPrinter? Testcode:

$$\ce{2H2 + O2 -> 2H2O}$$

$$\ce{2H2 + O2 -> 2H2O}$$

Enable mhchemmanually via $\require{mhchem}$ $\require{mhchem}$ and try again: $$\ce{2H2 + O2 -> 2H2O}$$

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$\mathcal{M}_{ath}\mathrm{J^{a}X}\neq\LaTeX$

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Operation Broken Arrow

$$\require{cancel}\ce{\bcancel{->}\cancel{->}\xcancel{->}}$$ $$%\require{Extpfeil}\Newextarrow{\xrightharpoonup}{5,10}{0x21C0}\xrightharpoonup{\not{}}$$ $$\nrightarrow$$ $$\ce{\rlap{~~/\!/}->}$$ $$\def\nnot{\color{red}{\rlap{~~/\!/}}}$$ $$\ce{\nnot->T[water]}$$

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$$\begin{multline} E^\ominus(\ce{Fe/Fe^{3+}}) - \frac13\cdot \mathcal{R}T\mathrm{F}^{-1} \ln\frac{\ce{Fe}}{\ce{Fe^{3+}}} = \\ a\cdot\left(E^\ominus(\ce{Fe/Fe^{2+}}) - \frac12\cdot \mathcal{R}T\mathrm{F}^{-1} \ln\frac{\ce{Fe}}{\ce{Fe^{2+}}}\right) \\+ b\cdot\left(E^\ominus(\ce{Fe^{2+}/Fe^{3+}}) - \frac11\cdot \mathcal{R}T\mathrm{F}^{-1} \ln\frac{\ce{Fe^{2+}}}{\ce{Fe^{3+}}}\right) \end{multline}$$

Heureka! Now I know how to use \begin{multline}...\end{multline} (enclose in $$).

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Let us add some colour by \color{\red}{...}:

$$\ce{\color{\red}{H}-\color{\green}{OH} + H2O <=>\color{\red}{H+}OH2 + \color{\green}{{}^{-}OH}} $$

• red $\ce{\color{\red}{H}}$
• navy $\ce{\color{\navy}{H}}$
• green $\ce{\color{\green}{H}}$
• orange $\ce{\color{\orange}{H}}$
• pink $\ce{\color{\pink}{H}}$
• purple $\ce{\color{\purple}{H}}$
• yellow $\ce{\color{\yellow}{H}}$
• white $\ce{\color{\white}{H}}$
• turquoise $\ce{\color{\turquoise}{H}}$
• but no blue $\ce{\color{\blue}{H}}$ - Why?

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$$\ce {4\overset{+I}{K}_2\overset{+VI}{Cr}_2\overset{-II}{O}_7 -> 4\overset{+I}{K}_2\overset{+VI}{Cr}\overset{-II}{O}_4 + 2\overset{+III}{Cr}_2\overset{-II}{O}_3 + 3\overset{\pm0}{O}_2}$$

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$\Tiny1\scriptsize2 \small3 \normalsize4 \large5 \Large6 \LARGE7 \huge8 \Huge9$

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$$\scriptstyle\Tiny \begin{array}{l|cccccccccccccccccc} \text{Gr.} &1 &2 &3 &4 &5 &6 &7 &8 &9 &10 &11 &12 &13 &14 &15 &16 &17 &18\\ \text{Per.}\\\hline 1& \ce{^1H} & &&&&&&&&&&&&&&&&\ce{^2He}\\ 2& \ce{^3Li}& \ce{^4Be}& &&&&&&&&&&\ce{^5B}& \ce{^6C}& \ce{^7N}& \ce{^8O}& \ce{^9F}& \ce{^{10}Ne}\\ 3& \ce{^{11}Na}& \ce{^{12}Mg}& &&&&&&&&&&\ce{^{13}Al}& \ce{^{14}Si}& \ce{^{15}P}& \ce{^{16}S}& \ce{^{17}Cl}& \ce{^{18}Ar}\\ 4& \ce{^{19}K}& \ce{^{20}Ca}& \ce{^{21}Sc}& \ce{^{22}Ti}& \ce{^{23}V}& \ce{^{24}Cr}& \ce{^{25}Mn}& \ce{^{26}Fe}& \ce{^{27}Co}& \ce{^{28}Ni}& \ce{^{29}Cu}& \ce{^{30}Zn}& \ce{^{31}Ga}& \ce{^{32}Ge}& \ce{^{33}As}& \ce{^{34}Se}& \ce{^{35}Br}& \ce{^{36}Kr}\\ 5& \ce{^{37}Rb}& \ce{^{38}Sr}& \ce{^{39}Y}& \ce{^{40}Zr}& \ce{^{41}Nb}& \ce{^{42}Mo}& \ce{^{43}Tc}& \ce{^{44}Ru}& \ce{^{45}Rh}& \ce{^{46}Pd}& \ce{^{47}Ag}& \ce{^{48}Cd}& \ce{^{49}In}& \ce{^{50}Sn}& \ce{^{51}Sb}& \ce{^{52}Te}& \ce{^{53}I}& \ce{^{54}Xe}\\ 6&\ce{^{55}Cs}& \ce{^{56}Ba}& \text{*}& \ce{^{72}Hf}& \ce{^{73}Ta}& \ce{^{74}W}& \ce{^{75}Re}& \ce{^{76}Os}& \ce{^{77}Ir}& \ce{^{78}Pt}& \ce{^{79}Au}& \ce{^{80}Hg}& \ce{^{81}Tl}& \ce{^{82}Pb}& \ce{^{83}Bi}& \ce{^{84}Po}& \ce{^{85}At}& \ce{^{86}Rn}\\ 7& \ce{^{87}Fr}& \ce{^{88}Ra}& \text{**}& \ce{^{104}Rf}& \ce{^{105}Db}& \ce{^{106}Sg}& \ce{^{107}Bh}& \ce{^{108}Hs}& \ce{^{109}Mt}& \ce{^{110}Ds}& \ce{^{111}Rg}& \ce{^{112}Cn}& \ce{^{113}Uut}& \ce{^{114}Fl}& \ce{^{115}Uup}& \ce{^{116}Lv}& \ce{^{117}Uus}& \ce{^{118}Uuo}\\\hline \end{array}\\ \scriptstyle\Tiny \begin{array}{lc} \text{* Lanthanoide}& \ce{^{57}La}& \ce{^{58}Ce}& \ce{^{59}Pr}& \ce{^{60}Nd}& \ce{^{61}Pm}& \ce{^{62}Sm}& \ce{^{63}Eu}& \ce{^{64}Gd}& \ce{^{65}Tb}& \ce{^{66}Dy}& \ce{^{67}Ho}& \ce{^{68}Er}& \ce{^{69}Tm}& \ce{^{70}Yb}& \ce{^{71}Lu}\\ \text{** Actinoide}& \ce{^{89}Ac}& \ce{^{90}Th}& \ce{^{91}Pa}& \ce{^{92}U}& \ce{^{93}Np}& \ce{^{94}Pu}& \ce{^{95}Am}& \ce{^{96}Cm}& \ce{^{97}Bk}& \ce{^{98}Cf}& \ce{^{99}Es}& \ce{^{100}Fm}& \ce{^{101}Md}& \ce{^{102}No}& \ce{^{103}Lr} \\ \end{array}$$

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Can I haz two labels in one alignment? \begin{align} A&=B\tag{1}\\ B&=C\tag{2}\\\hline A&=C\tag{1 = 2} \end{align}

Yes, we can!

Escape math in tags \tag{$\alpha$} \begin{align} A&=B\tag{$\alpha$}\\ B&=C\tag{$\beta$}\\\hline A&=C\tag{$\alpha = \beta$} \end{align}

Answer 4

This is a trick for homework question, show answer only with mouseover! (pass mouse over the gray box to see the answer)

How can I do that?

with >!

Answer 5

$$\ce{ 2H_2O <- Ò˛Ò -> 4H + O_2 } $$

Answer 6

$$\ce{DCB ->C[{h\nu}]\ ^1DCB^{\ast}}$$ $$\ce{^1DCB^{\ast} + BP -> DCB^{.-} +BP^{.+}}$$

\[ J(\phi) = \mathrm{A} \cos^2\phi + \mathrm{B} \cos\phi + \mathrm{C} \]

\begin{eqnarray} f(x) & = & \underbrace{x^{2}+2x+1}\\ & & \quad(x+1)^ 2 \end{eqnarray}

$$123.45\,\times 10^{-6}$$

Colours defined outside the \ce{...} environment

Some dvipsnames for colours seem to work

Salmon $\color{Salmon}{\ce{Ni(CO)4}}$

Maroon $\color{Maroon}{\ce{A + B <=>> C}}$

CadetBlue $\color{CadetBlue}{\ce{C=C-C+ <->\ ^{+}C-C=C}}$

CornflowerBlue $\color{CornflowerBlue}{\ce{C=C-C+ <->\ ^{+}C-C=C}}$

Answer 7

Quantities and units

$$\small \begin{array}{llll} \hline \text{Quantity} & \text{Quantity} & \text{Unit} & \text{Unit} \\ \text{name} & \text{symbol} & \text{name} & \text{symbol} \\ \hline \text{volume} & V & \text{cubic metre} & \mathrm{m^3} \\ \text{time, duration} & t & \text{second} & \mathrm{s} \\ \text{frequency} & f, \nu & \text{hertz} & \mathrm{Hz} \\ \text{wavelength} & \lambda & \text{metre} & \mathrm{m} \\ \text{wavenumber, repetency} & \sigma, \tilde \nu & \text{metre to the power minus one} & \mathrm{m^{-1}} \\ \text{mass} & m & \text{kilogram} & \mathrm{kg} \\ \text{mass density, density} & \rho & \text{kilogram per cubic metre} & \mathrm{kg/m^3} \\ \text{pressure} & p & \text{pascal} & \mathrm{Pa} \\ \text{work} & W & \text{joule} & \mathrm{J} \\ %5. Thermodynamics% \text{thermodynamic temperature} & T & \text{kelvin} & \mathrm{K} \\%5-1% \text{Celsius temperature} & t,\vartheta & \text{degree Celsius} & \mathrm{^\circ C} \\%5-2% \text{heat, amount of heat} & Q & \text{joule} & \mathrm{J} \\ \text{heat capacity} & C & \text{joule per kelvin} & \mathrm{J/K} \\ \text{specific heat capacity} & c & \text{joule per kilogram kelvin} & \mathrm{J/( kg \cdot K )} \\ \text{specific heat capacity at constant pressure} & c_p & \text{joule per kilogram kelvin} & \mathrm{J/( kg \cdot K )} \\%5-16.2% \text{specific heat capacity at constant volume} & c_V & \text{joule per kilogram kelvin} & \mathrm{J/( kg \cdot K )} \\%5-16.3% \text{ratio of the specific heat capacities} & \gamma & \text{one} & 1 \\%5-17% \text{entropy} & S & \text{joule per kelvin} & \mathrm{J/K} \\ \text{specific entropy} & s & \text{joule per kilogram kelvin} & \mathrm{J/( kg \cdot K )} \\ \text{energy} & E & \text{joule} & \mathrm{J} \\ \text{internal energy, thermodynamic energy} & U & \text{joule} & \mathrm{J} \\ \text{enthalpy} & H & \text{joule} & \mathrm{J} \\ \text{Helmholtz energy, Helmholtz function} & A, F & \text{joule} & \mathrm{J} \\ \text{Gibbs energy, Gibbs function} & G & \text{joule} & \mathrm{J} \\ %9. Physical chemistry and molecular physics% \text{amount of substance} & n & \text{mole} & \mathrm{mol} \\%9-1% \text{relative atomic mass} & A_\mathrm r & \text{one} & \mathrm{1} \\ \text{relative molecular mass} & M_\mathrm r & \text{one} & \mathrm{1} \\ \text{Avogadro constant} & L,N_\mathrm A & \text{mole to the power minus one} & \mathrm{mol^{-1}} \\%9-4% \text{molar mass} & M & \text{kilogram per mole} & \mathrm{kg/mol} \\%9-5% \text{molar volume} & V_\mathrm m & \text{cubic metre per mole} & \mathrm{m^3/mol} \\%9-6% \text{molar heat capacity} & C_\mathrm m & \text{joule per mole kelvin} & \mathrm{J/( mol \cdot K )} \\%9-8% \text{molar heat capacity at constant pressure} & C_{\mathrm m, p} & \text{joule per mole kelvin} & \mathrm{J/( mol \cdot K )} \\ \text{molar heat capacity at constant volume} & C_{\mathrm m, V} & \text{joule per mole kelvin} & \mathrm{J/( mol \cdot K )} \\ \text{amount-of-substance concentration,} & c & \text{mole per cubic metre} & \mathrm{mol/m^3} \\%9-13% \text{concentration} & & & \\ \text{molar gas constant} & R & \text{joule per mole kelvin} & \mathrm{J/(mol\cdot K)} \\%9-42% \text{Boltzmann constant} & k & \text{joule per kelvin} & \mathrm{J/K} \\%9-42% \text{Faraday constant} & F & \text{coulomb per mole} & \mathrm{C/mol} \\%9-51% \text{Planck constant} & h & \text{joule second} & \mathrm{J\cdot s} \\%10-6.1% \text{reduced Planck constant} & \hbar & \text{joule second} & \mathrm{J\cdot s} \\%10-6.2% \hline \end{array}$$

 

$$\textbf{Non-SI units accepted for use with the International System of Units}\\ \small \begin{array}{lll} \hline \text{Quantity} & \text{Unit} & \text{Unit} \\ \text{name} & \text{name} & \text{symbol} \\ \hline \text{time} & \text{minute} & \mathrm{min} \\ & \text{hour} & \mathrm{h} \\ & \text{day} & \mathrm{d} \\ \text{plane angle} & \text{degree} & ^\circ \\ & \text{minute} & ' \\ & \text{second} & '' \\ \text{volume} & \text{litre} & \mathrm{l} \\ \text{energy} & \text{electronvolt} & \mathrm{eV} \\ \text{mass} & \text{dalton} & \mathrm{Da} \\ & \text{unified atomic mass unit} & \mathrm{u} \\ \hline \end{array}$$

 

$$\textbf{Other non-SI units}\\ \small \begin{array}{lll} \hline \text{Quantity} & \text{Unit} & \text{Unit} \\ \text{name} & \text{name} & \text{symbol} \\ \hline \text{pressure} & \text{bar} & \mathrm{bar} \\ \text{length} & \mathrm{\overset{\circ}a}\text{ngstr}\mathrm{\ddot o}\text{m} & \mathrm{\mathring{A}} \\ \text{area} & \text{barn} & \mathrm{b} \\ \hline \end{array}$$

 

$$\textbf{Other non-SI units given for information}\\ \text{The use of these units is deprecated.}\\ \small \begin{array}{lll} \hline \text{Quantity} & \text{Unit} & \text{Unit} \\ \text{name} & \text{name} & \text{symbol} \\ \hline \text{heat, amount of heat} & \text{calorie} & \mathrm{cal} \\ \text{pressure} & \text{standard atmosphere} & \mathrm{atm} \\ & \text{conventional millimetre of mercury} & \mathrm{mmHg} \\ & \text{torr} & \text{Torr} \\ & \text{pound-force per square inch} & \text{psi} \\ \text{temperature} & \text{degree Rankine} & \mathrm{^\circ R} \\ & \text{degree Fahrenheit} & \mathrm{^\circ F} \\ \text{mass} & \text{atomic mass unit} & \mathrm{amu} \\ \hline \end{array}$$

Answer 8

$\ce{H2O + HCl->H3O+ + Cl-}$

$\ce{RC6H6\frac{XeF2}{->}Rc6H5f + Xe + HF}$

\xrightarrow{n,n}

$\ce{RC6H6\xrightarrow{XeF2} Rc6H5f + Xe + HF}$

Hmmm, too bad the \xrightarrow{XeF2} looks ugly!

Answer 9

$\ce{CH2=HC-C#O}$

$\ce{R=C=O}$

$\ce{A\bond{~}B\bond{~-}C}$

$\ce{^{238}_{92}U\,+n->^{239}_{92}U\,+\gamma }$

$\ce{$cis${-}[PtCl2(NH3)2]}$

$\ce{-(C2H4)n -}$

Answer 10

I just need my own thread to get on no one's nerves.

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$d_\pi-p_\pi$ $d_\pi-p_\pi$

$d_\pi{-}p_\pi$ $d_\pi{-}p_\pi$

$\mathrm{d_\pi-p_\pi}$ $\mathrm{d_\pi-p_\pi}$

$\mathrm{d_\pi{-}p_\pi}$ $\mathrm{d_\pi{-}p_\pi}$

$\ce{d_\pi-p_\pi}$ $\ce{d_\pi-p_\pi}$

$\ce{d_\pi{-}p_\pi}$ $\ce{d_\pi{-}p_\pi}$

$\ce{d_\pi\hyphen p_\pi}$ $\ce{d_\pi\hyphen p_\pi}$

Answer 11

Warning: This relies on fonts used in the user's computer. Use at your own risk.

But seriously, how many computers today don't have fonts like Times not installed?

Using the Unicode macro is a workaround we could use to produce upright Greek letters. However, the font sizes are not guaranteed to work with Mathjax; thus, you may need to resize them when necessary.

Note that declaring a font is in brackets; that means it's optional and it most likely will work without a [Times]; but adding that font option is recommended since then you'd make sure the font is available and the rendering is what you expect it to be. If your code is getting too long, you could leave it out.

The syntax is \unicode[<font face>]{<some bizarre code>}. Here goes:

Upright lowercase alpha (U+03B1)

\tiny\unicode[Times]{x3B1} $\Longrightarrow ~ \tiny\unicode[Times]{x3B1}$ Normal text
\small\unicode[Times]{x3B1} $\Longrightarrow ~ \small\unicode[Times]{x3B1}$ Normal text
\unicode[Times]{x3B1} $\Longrightarrow ~ \unicode[Times]{x3B1}$ Normal text
\large\unicode[Times]{x3B1} $\Longrightarrow ~ \large\unicode[Times]{x3B1}$ Normal text
\Large\unicode[Times]{x3B1} $\Longrightarrow ~ \Large\unicode[Times]{x3B1}$ Normal text
\huge\unicode[Times]{x3B1} $\Longrightarrow ~ \huge\unicode[Times]{x3B1}$ Normal text
\Huge\unicode[Times]{x3B1} $\Longrightarrow ~ \Huge\unicode[Times]{x3B1}$ Normal text

Upright lowercase beta (U+03B2)

\tiny\unicode[Times]{x3B2} $\Longrightarrow ~ \tiny\unicode[Times]{x3B2}$ Normal text
\small\unicode[Times]{x3B2} $\Longrightarrow ~ \small\unicode[Times]{x3B2}$ Normal text
\unicode[Times]{x3B2} $\Longrightarrow ~ \unicode[Times]{x3B2}$ Normal text
\large\unicode[Times]{x3B2} $\Longrightarrow ~ \large\unicode[Times]{x3B2}$ Normal text
\Large\unicode[Times]{x3B2} $\Longrightarrow ~ \Large\unicode[Times]{x3B2}$ Normal text
\huge\unicode[Times]{x3B2} $\Longrightarrow ~ \huge\unicode[Times]{x3B2}$ Normal text
\Huge\unicode[Times]{x3B2} $\Longrightarrow ~ \Huge\unicode[Times]{x3B2}$ Normal text

Upright lowercase gamma (U+03B3)

\tiny\unicode[Times]{x3B3} $\Longrightarrow ~ \tiny\unicode[Times]{x3B3}$ Normal text
\small\unicode[Times]{x3B3} $\Longrightarrow ~ \small\unicode[Times]{x3B3}$ Normal text
\unicode[Times]{x3B3} $\Longrightarrow ~ \unicode[Times]{x3B3}$ Normal text
\large\unicode[Times]{x3B3} $\Longrightarrow ~ \large\unicode[Times]{x3B3}$ Normal text
\Large\unicode[Times]{x3B3} $\Longrightarrow ~ \Large\unicode[Times]{x3B3}$ Normal text
\huge\unicode[Times]{x3B3} $\Longrightarrow ~ \huge\unicode[Times]{x3B3}$ Normal text
\Huge\unicode[Times]{x3B3} $\Longrightarrow ~ \Huge\unicode[Times]{x3B3}$ Normal text

Upright lowercase delta (U+03B4)

\tiny\unicode[Times]{x3B4} $\Longrightarrow ~ \tiny\unicode[Times]{x3B4}$ Normal text
\small\unicode[Times]{x3B4} $\Longrightarrow ~ \small\unicode[Times]{x3B4}$ Normal text
\unicode[Times]{x3B4} $\Longrightarrow ~ \unicode[Times]{x3B4}$ Normal text
\large\unicode[Times]{x3B4} $\Longrightarrow ~ \large\unicode[Times]{x3B4}$ Normal text
\Large\unicode[Times]{x3B4} $\Longrightarrow ~ \Large\unicode[Times]{x3B4}$ Normal text
\huge\unicode[Times]{x3B4} $\Longrightarrow ~ \huge\unicode[Times]{x3B4}$ Normal text
\Huge\unicode[Times]{x3B4} $\Longrightarrow ~ \Huge\unicode[Times]{x3B4}$ Normal text

Upright lowercase epsilon (U+03B5)

\tiny\unicode[Times]{x3B5} $\Longrightarrow ~ \tiny\unicode[Times]{x3B5}$ Normal text
\small\unicode[Times]{x3B5} $\Longrightarrow ~ \small\unicode[Times]{x3B5}$ Normal text
\unicode[Times]{x3B5} $\Longrightarrow ~ \unicode[Times]{x3B5}$ Normal text
\large\unicode[Times]{x3B5} $\Longrightarrow ~ \large\unicode[Times]{x3B5}$ Normal text
\Large\unicode[Times]{x3B5} $\Longrightarrow ~ \Large\unicode[Times]{x3B5}$ Normal text
\huge\unicode[Times]{x3B5} $\Longrightarrow ~ \huge\unicode[Times]{x3B5}$ Normal text
\Huge\unicode[Times]{x3B5} $\Longrightarrow ~ \Huge\unicode[Times]{x3B5}$ Normal text

Upright lowercase zeta (U+03B6)

\tiny\unicode[Times]{x3B6} $\Longrightarrow ~ \tiny\unicode[Times]{x3B6}$ Normal text
\small\unicode[Times]{x3B6} $\Longrightarrow ~ \small\unicode[Times]{x3B6}$ Normal text
\unicode[Times]{x3B6} $\Longrightarrow ~ \unicode[Times]{x3B6}$ Normal text
\large\unicode[Times]{x3B6} $\Longrightarrow ~ \large\unicode[Times]{x3B6}$ Normal text
\Large\unicode[Times]{x3B6} $\Longrightarrow ~ \Large\unicode[Times]{x3B6}$ Normal text
\huge\unicode[Times]{x3B6} $\Longrightarrow ~ \huge\unicode[Times]{x3B6}$ Normal text
\Huge\unicode[Times]{x3B6} $\Longrightarrow ~ \Huge\unicode[Times]{x3B6}$ Normal text

Upright lowercase eta (U+03B7)

\tiny\unicode[Times]{x3B7} $\Longrightarrow ~ \tiny\unicode[Times]{x3B7}$ Normal text
\small\unicode[Times]{x3B7} $\Longrightarrow ~ \small\unicode[Times]{x3B7}$ Normal text
\unicode[Times]{x3B7} $\Longrightarrow ~ \unicode[Times]{x3B7}$ Normal text
\large\unicode[Times]{x3B7} $\Longrightarrow ~ \large\unicode[Times]{x3B7}$ Normal text
\Large\unicode[Times]{x3B7} $\Longrightarrow ~ \Large\unicode[Times]{x3B7}$ Normal text
\huge\unicode[Times]{x3B7} $\Longrightarrow ~ \huge\unicode[Times]{x3B7}$ Normal text
\Huge\unicode[Times]{x3B7} $\Longrightarrow ~ \Huge\unicode[Times]{x3B7}$ Normal text

Upright lowercase theta (U+03B8)

\tiny\unicode[Times]{x3B8} $\Longrightarrow ~ \tiny\unicode[Times]{x3B8}$ Normal text
\small\unicode[Times]{x3B8} $\Longrightarrow ~ \small\unicode[Times]{x3B8}$ Normal text
\unicode[Times]{x3B8} $\Longrightarrow ~ \unicode[Times]{x3B8}$ Normal text
\large\unicode[Times]{x3B8} $\Longrightarrow ~ \large\unicode[Times]{x3B8}$ Normal text
\Large\unicode[Times]{x3B8} $\Longrightarrow ~ \Large\unicode[Times]{x3B8}$ Normal text
\huge\unicode[Times]{x3B8} $\Longrightarrow ~ \huge\unicode[Times]{x3B8}$ Normal text
\Huge\unicode[Times]{x3B8} $\Longrightarrow ~ \Huge\unicode[Times]{x3B8}$ Normal text

Upright lowercase iota (U+03B9)

\tiny\unicode[Times]{x3B9} $\Longrightarrow ~ \tiny\unicode[Times]{x3B9}$ Normal text
\small\unicode[Times]{x3B9} $\Longrightarrow ~ \small\unicode[Times]{x3B9}$ Normal text
\unicode[Times]{x3B9} $\Longrightarrow ~ \unicode[Times]{x3B9}$ Normal text
\large\unicode[Times]{x3B9} $\Longrightarrow ~ \large\unicode[Times]{x3B9}$ Normal text
\Large\unicode[Times]{x3B9} $\Longrightarrow ~ \Large\unicode[Times]{x3B9}$ Normal text
\huge\unicode[Times]{x3B9} $\Longrightarrow ~ \huge\unicode[Times]{x3B9}$ Normal text
\Huge\unicode[Times]{x3B9} $\Longrightarrow ~ \Huge\unicode[Times]{x3B9}$ Normal text

Upright lowercase kappa (U+03BA)

\tiny\unicode[Times]{x3BA} $\Longrightarrow ~ \tiny\unicode[Times]{x3BA}$ Normal text
\small\unicode[Times]{x3BA} $\Longrightarrow ~ \small\unicode[Times]{x3BA}$ Normal text
\unicode[Times]{x3BA} $\Longrightarrow ~ \unicode[Times]{x3BA}$ Normal text
\large\unicode[Times]{x3BA} $\Longrightarrow ~ \large\unicode[Times]{x3BA}$ Normal text
\Large\unicode[Times]{x3BA} $\Longrightarrow ~ \Large\unicode[Times]{x3BA}$ Normal text
\huge\unicode[Times]{x3BA} $\Longrightarrow ~ \huge\unicode[Times]{x3BA}$ Normal text
\Huge\unicode[Times]{x3BA $\Longrightarrow ~ \Huge\unicode[Times]{x3BA}$ Normal text

Upright lowercase lambda (U+03BB)

\tiny\unicode[Times]{x3BB} $\Longrightarrow ~ \tiny\unicode[Times]{x3BB}$ Normal text
\small\unicode[Times]{x3BB} $\Longrightarrow ~ \small\unicode[Times]{x3BB}$ Normal text
\unicode[Times]{x3BB} $\Longrightarrow ~ \unicode[Times]{x3BB}$ Normal text
\large\unicode[Times]{x3BB} $\Longrightarrow ~ \large\unicode[Times]{x3BB}$ Normal text
\Large\unicode[Times]{x3BB} $\Longrightarrow ~ \Large\unicode[Times]{x3BB}$ Normal text
\huge\unicode[Times]{x3BB} $\Longrightarrow ~ \huge\unicode[Times]{x3BB}$ Normal text
\Huge\unicode[Times]{x3BB} $\Longrightarrow ~ \Huge\unicode[Times]{x3BB}$ Normal text

Upright lowercase mu (U+03BC)

\tiny\unicode[Times]{x3BC} $\Longrightarrow ~ \tiny\unicode[Times]{x3BC}$ Normal text
\small\unicode[Times]{x3BC} $\Longrightarrow ~ \small\unicode[Times]{x3BC}$ Normal text
\unicode[Times]{x3BC} $\Longrightarrow ~ \unicode[Times]{x3BC}$ Normal text
\large\unicode[Times]{x3BC} $\Longrightarrow ~ \large\unicode[Times]{x3BC}$ Normal text
\Large\unicode[Times]{x3BC} $\Longrightarrow ~ \Large\unicode[Times]{x3BC}$ Normal text
\huge\unicode[Times]{x3BC} $\Longrightarrow ~ \huge\unicode[Times]{x3BC}$ Normal text
\Huge\unicode[Times]{x3BC} $\Longrightarrow ~ \Huge\unicode[Times]{x3BC}$ Normal text

Upright lowercase nu (U+03BD)

\tiny\unicode[Times]{x3BD} $\Longrightarrow ~ \tiny\unicode[Times]{x3BD}$ Normal text
\small\unicode[Times]{x3BD} $\Longrightarrow ~ \small\unicode[Times]{x3BD}$ Normal text
\unicode[Times]{x3BD} $\Longrightarrow ~ \unicode[Times]{x3BD}$ Normal text
\large\unicode[Times]{x3BD} $\Longrightarrow ~ \large\unicode[Times]{x3BD}$ Normal text
\Large\unicode[Times]{x3BD} $\Longrightarrow ~ \Large\unicode[Times]{x3BD}$ Normal text
\huge\unicode[Times]{x3BD} $\Longrightarrow ~ \huge\unicode[Times]{x3BD}$ Normal text
\Huge\unicode[Times]{x3BD} $\Longrightarrow ~ \Huge\unicode[Times]{x3BD}$ Normal text

Upright lowercase xi (U+03BE)

\tiny\unicode[Times]{x3BE} $\Longrightarrow ~ \tiny\unicode[Times]{x3BE}$ Normal text
\small\unicode[Times]{x3BE} $\Longrightarrow ~ \small\unicode[Times]{x3BE}$ Normal text
\unicode[Times]{x3BE} $\Longrightarrow ~ \unicode[Times]{x3BE}$ Normal text
\large\unicode[Times]{x3BE} $\Longrightarrow ~ \large\unicode[Times]{x3BE}$ Normal text
\Large\unicode[Times]{x3BE} $\Longrightarrow ~ \Large\unicode[Times]{x3BE}$ Normal text
\huge\unicode[Times]{x3BE} $\Longrightarrow ~ \huge\unicode[Times]{x3BE}$ Normal text
\Huge\unicode[Times]{x3BE} $\Longrightarrow ~ \Huge\unicode[Times]{x3BE}$ Normal text

Upright lowercase omicron (U+03BF)

\tiny\unicode[Times]{x3BF} $\Longrightarrow ~ \tiny\unicode[Times]{x3BF}$ Normal text
\small\unicode[Times]{x3BF} $\Longrightarrow ~ \small\unicode[Times]{x3BF}$ Normal text
\unicode[Times]{x3BF} $\Longrightarrow ~ \unicode[Times]{x3BF}$ Normal text
\large\unicode[Times]{x3BF} $\Longrightarrow ~ \large\unicode[Times]{x3BF}$ Normal text
\Large\unicode[Times]{x3BF} $\Longrightarrow ~ \Large\unicode[Times]{x3BF}$ Normal text
\huge\unicode[Times]{x3BF} $\Longrightarrow ~ \huge\unicode[Times]{x3BF}$ Normal text
\Huge\unicode[Times]{x3BF} $\Longrightarrow ~ \Huge\unicode[Times]{x3BF}$ Normal text

Upright lowercase pi (U+03C0)

\tiny\unicode[Times]{x3C0} $\Longrightarrow ~ \tiny\unicode[Times]{x3C0}$ Normal text
\small\unicode[Times]{x3C0} $\Longrightarrow ~ \small\unicode[Times]{x3C0}$ Normal text
\unicode[Times]{x3C0} $\Longrightarrow ~ \unicode[Times]{x3C0}$ Normal text
\large\unicode[Times]{x3C0} $\Longrightarrow ~ \large\unicode[Times]{x3C0}$ Normal text
\Large\unicode[Times]{x3C0} $\Longrightarrow ~ \Large\unicode[Times]{x3C0}$ Normal text
\huge\unicode[Times]{x3C0} $\Longrightarrow ~ \huge\unicode[Times]{x3C0}$ Normal text
\Huge\unicode[Times]{x3C0} $\Longrightarrow ~ \Huge\unicode[Times]{x3C0}$ Normal text

Upright lowercase rho (U+03C1)

\tiny\unicode[Times]{x3C1} $\Longrightarrow ~ \tiny\unicode[Times]{x3C1}$ Normal text
\small\unicode[Times]{x3C1} $\Longrightarrow ~ \small\unicode[Times]{x3C1}$ Normal text
\unicode[Times]{x3C1} $\Longrightarrow ~ \unicode[Times]{x3C1}$ Normal text
\large\unicode[Times]{x3C1} $\Longrightarrow ~ \large\unicode[Times]{x3C1}$ Normal text
\Large\unicode[Times]{x3C1} $\Longrightarrow ~ \Large\unicode[Times]{x3C1}$ Normal text
\huge\unicode[Times]{x3C1} $\Longrightarrow ~ \huge\unicode[Times]{x3C1}$ Normal text
\Huge\unicode[Times]{x3C1} $\Longrightarrow ~ \Huge\unicode[Times]{x3C1}$ Normal text

Upright lowercase final sigma (U+03C2)

\tiny\unicode[Times]{x3C2} $\Longrightarrow ~ \tiny\unicode[Times]{x3C2}$ Normal text
\small\unicode[Times]{x3C2} $\Longrightarrow ~ \small\unicode[Times]{x3C2}$ Normal text
\unicode[Times]{x3C2} $\Longrightarrow ~ \unicode[Times]{x3C2}$ Normal text
\large\unicode[Times]{x3C2} $\Longrightarrow ~ \large\unicode[Times]{x3C2}$ Normal text
\Large\unicode[Times]{x3C2} $\Longrightarrow ~ \Large\unicode[Times]{x3C2}$ Normal text
\huge\unicode[Times]{x3C2} $\Longrightarrow ~ \huge\unicode[Times]{x3C2}$ Normal text
\Huge\unicode[Times]{x3C2} $\Longrightarrow ~ \Huge\unicode[Times]{x3C2}$ Normal text

Upright lowercase sigma (U+03C3)

\tiny\unicode[Times]{x3C3} $\Longrightarrow ~ \tiny\unicode[Times]{x3C3}$ Normal text
\small\unicode[Times]{x3C3} $\Longrightarrow ~ \small\unicode[Times]{x3C3}$ Normal text
\unicode[Times]{x3C3} $\Longrightarrow ~ \unicode[Times]{x3C3}$ Normal text
\large\unicode[Times]{x3C3} $\Longrightarrow ~ \large\unicode[Times]{x3C3}$ Normal text
\Large\unicode[Times]{x3C3} $\Longrightarrow ~ \Large\unicode[Times]{x3C3}$ Normal text
\huge\unicode[Times]{x3C3} $\Longrightarrow ~ \huge\unicode[Times]{x3C3}$ Normal text
\Huge\unicode[Times]{x3C3} $\Longrightarrow ~ \Huge\unicode[Times]{x3C3}$ Normal text

Upright lowercase tau (U+03C4)

\tiny\unicode[Times]{x3C4} $\Longrightarrow ~ \tiny\unicode[Times]{x3C4}$ Normal text
\small\unicode[Times]{x3C4} $\Longrightarrow ~ \small\unicode[Times]{x3C4}$ Normal text
\unicode[Times]{x3C4} $\Longrightarrow ~ \unicode[Times]{x3C4}$ Normal text
\large\unicode[Times]{x3C4} $\Longrightarrow ~ \large\unicode[Times]{x3C4}$ Normal text
\Large\unicode[Times]{x3C4} $\Longrightarrow ~ \Large\unicode[Times]{x3C4}$ Normal text
\huge\unicode[Times]{x3C4} $\Longrightarrow ~ \huge\unicode[Times]{x3C4}$ Normal text
\Huge\unicode[Times]{x3C4} $\Longrightarrow ~ \Huge\unicode[Times]{x3C4}$ Normal text

Upright lowercase upsilon (U+03C5)

\tiny\unicode[Times]{x3C5} $\Longrightarrow ~ \tiny\unicode[Times]{x3C5}$ Normal text
\small\unicode[Times]{x3C5} $\Longrightarrow ~ \small\unicode[Times]{x3C5}$ Normal text
\unicode[Times]{x3C5} $\Longrightarrow ~ \unicode[Times]{x3C5}$ Normal text
\large\unicode[Times]{x3C5} $\Longrightarrow ~ \large\unicode[Times]{x3C5}$ Normal text
\Large\unicode[Times]{x3C5} $\Longrightarrow ~ \Large\unicode[Times]{x3C5}$ Normal text
\huge\unicode[Times]{x3C5} $\Longrightarrow ~ \huge\unicode[Times]{x3C5}$ Normal text
\Huge\unicode[Times]{x3C5} $\Longrightarrow ~ \Huge\unicode[Times]{x3C5}$ Normal text

Upright lowercase phi (U+03C6)

\tiny\unicode[Times]{x3C6} $\Longrightarrow ~ \tiny\unicode[Times]{x3C6}$ Normal text
\small\unicode[Times]{x3C6} $\Longrightarrow ~ \small\unicode[Times]{x3C6}$ Normal text
\unicode[Times]{x3C6} $\Longrightarrow ~ \unicode[Times]{x3C6}$ Normal text
\large\unicode[Times]{x3C6} $\Longrightarrow ~ \large\unicode[Times]{x3C6}$ Normal text
\Large\unicode[Times]{x3C6} $\Longrightarrow ~ \Large\unicode[Times]{x3C6}$ Normal text
\huge\unicode[Times]{x3C6} $\Longrightarrow ~ \huge\unicode[Times]{x3C6}$ Normal text
\Huge\unicode[Times]{x3C6} $\Longrightarrow ~ \Huge\unicode[Times]{x3C6}$ Normal text

Upright lowercase chi (U+03C7)

\tiny\unicode[Times]{x3C7} $\Longrightarrow ~ \tiny\unicode[Times]{x3C7}$ Normal text
\small\unicode[Times]{x3C7} $\Longrightarrow ~ \small\unicode[Times]{x3C7}$ Normal text
\unicode[Times]{x3C7} $\Longrightarrow ~ \unicode[Times]{x3B1}$ Normal text
\large\unicode[Times]{x3C7} $\Longrightarrow ~ \large\unicode[Times]{x3C7}$ Normal text
\Large\unicode[Times]{x3C7} $\Longrightarrow ~ \Large\unicode[Times]{x3C7}$ Normal text
\huge\unicode[Times]{x3C7} $\Longrightarrow ~ \huge\unicode[Times]{x3C7}$ Normal text
\Huge\unicode[Times]{x3C7} $\Longrightarrow ~ \Huge\unicode[Times]{x3C7}$ Normal text

Upright lowercase psi (U+03C8)

\tiny\unicode[Times]{x3C8} $\Longrightarrow ~ \tiny\unicode[Times]{x3C8}$ Normal text
\small\unicode[Times]{x3C8} $\Longrightarrow ~ \small\unicode[Times]{x3C8}$ Normal text
\unicode[Times]{x3C8} $\Longrightarrow ~ \unicode[Times]{x3C8}$ Normal text
\large\unicode[Times]{x3C8} $\Longrightarrow ~ \large\unicode[Times]{x3C8}$ Normal text
\Large\unicode[Times]{x3C8} $\Longrightarrow ~ \Large\unicode[Times]{x3C8}$ Normal text
\huge\unicode[Times]{x3C8} $\Longrightarrow ~ \huge\unicode[Times]{x3C8}$ Normal text
\Huge\unicode[Times]{x3C8} $\Longrightarrow ~ \Huge\unicode[Times]{x3C8}$ Normal text

Upright lowercase omega (U+03C9)

\tiny\unicode[Times]{x3C9} $\Longrightarrow ~ \tiny\unicode[Times]{x3C9}$ Normal text
\small\unicode[Times]{x3C9} $\Longrightarrow ~ \small\unicode[Times]{x3C9}$ Normal text
\unicode[Times]{x3C9} $\Longrightarrow ~ \unicode[Times]{x3C9}$ Normal text
\large\unicode[Times]{x3C9} $\Longrightarrow ~ \large\unicode[Times]{x3C9}$ Normal text
\Large\unicode[Times]{x3C9} $\Longrightarrow ~ \Large\unicode[Times]{x3C9}$ Normal text
\huge\unicode[Times]{x3C9} $\Longrightarrow ~ \huge\unicode[Times]{x3C9}$ Normal text
\Huge\unicode[Times]{x3C9} $\Longrightarrow ~ \Huge\unicode[Times]{x3C9}$ Normal text

Answer 12

Miscellaneous signs and symbols

• $a$ is equal to $b$

  $$a = b$$

• $a$ is not equal to $b$

  $$a \ne b$$

• $a$ corresponds to $b$

  $$a \overset{\wedge}{=}b$$

• $a$ is approximately equal to $b$

  $$a \approx b$$

• $a$ is asymptotically equal to $b$

  $$a \simeq b$$

• $a$ is proportional to $b$

  $$a \sim b$$ The notation $a \propto b$ is also used.

• $a$ is less than $b$

  $$a \lt b$$

• $b$ is greater than $a$

  $$b \gt a$$

• $a$ is less than or equal to $b$

  $$a \leqslant b$$ The notation $a \leq b$ is also used in some standards.

• $b$ is greater than or equal to $a$

  $$b \geqslant a$$ The notation $b \geq a$ is also used in some standards.

• $a$ is much less than $b$

  $$a \ll b$$

• $b$ is much greater than $a$

  $$b \gg a$$

• infinity

  $$\infty $$

Answer 13

1. Normal resolution, normal size:

   

2. Normal resolution, “forced” to normal size:

   

3. Double resolution, forced to half size:

   

(To better see the difference, use the zoom feature in your web browser.)

Answer 14

WCl$_{6}$, WCl$_{14}$, WCl$_{18}$, and WCl$_{21}$. blah blah

Answer 15

Predefined colors are limited. ಠ_ಠ I hate limits. (´◣д◢`+) But, fear not my internet friends, for we have $\mathrm{\color{red}{R}\color{green}{G}\color{blue}{B}}$.

For those not in the know. So let's get colorful: \begin{array}{|c:c|c:c|c:c|} \hline \#000000 & {\rm \small \color{#000000}{Black}} & \#000000 & {\rm \small \color{#000000}{Black}} & \#000000 & {\rm \small \color{#000000}{Black}} \\\hline \#222222 & {\rm \small\color{#222222}{Very~dark~gray}} & \#220000 & {\rm \small \color{#220000}{Darker~red}} & \#002200 & {\rm \small \color{#002200}{Darker~green}}\\\hline \#444444 & {\rm \small\color{#444444}{Dark~gray}} & \#440000 & {\rm \small \color{#440000}{Darker~red}} & \#004400 & {\rm \small \color{#004400}{Darker~green}}\\\hline \#666666 & {\rm \small\color{#666666}{A~tad~bit~dark~gray}} & \#660000 & {\rm \small \color{#660000}{Darker~red}} & \#006600 & {\rm \small \color{#006600}{Darker~green}}\\\hline \#888888 & {\rm \small\color{#888888}{Gray}} & \#880000 & {\rm \small \color{#880000}{Darker~red}} & \#008800 & {\rm \small \color{#008800}{Darker~green}}\\\hline \#999999 & {\rm \small\color{#999999}{A~tad~bit~light~gray}} & \#990000 & {\rm \small \color{#990000}{Darker~red}} & \#009900 & {\rm \small \color{#009900}{Darker~green}}\\\hline \#aaaaaa & {\rm \small\color{#aaaaaa}{Light~gray}} & \#aa0000 & {\rm \small \color{#aa0000}{Darker~red}} & \#00aa00 & {\rm \small \color{#00aa00}{Darker~green}}\\\hline \#bbbbbb & {\rm \small\color{#bbbbbb}{Very~light~gray}} & \#bb0000 & {\rm \small \color{#bb0000}{Darker~red}} & \#00bb00 & {\rm \small \color{#00bb00}{Darker~green}}\\\hline \#cccccc & {\rm \small\color{#cccccc}{White{-}ish~gray}} & \#cc0000 & {\rm \small \color{#cc0000}{Darker~red}} & \#00cc00 & {\rm \small \color{#00cc00}{Darker~green}}\\\hline \#dddddd & {\rm \small\color{#dddddd}{Impure~white}} & \#dd0000 & {\rm \small \color{#dd0000}{Darker~red}} & \#00dd00 & {\rm \small \color{#00dd00}{Darker~green}}\\\hline \#eeeeee & {\rm \small\color{#eeeeee}{Black \, (?)}} & \#ee0000 & {\rm \small \color{#ee0000}{Darker~red}} & \#00ee00 & {\rm \small \color{#00ee00}{Darker~green}}\\\hline \#ffffff & {\rm \small\mathbb{WHITE}} & \#ff0000 & {\rm \small \color{#ff0000}{Purest~red}} & \#00ff00 & {\rm \small \color{#00ff00}{Purest~green}}\\\hline \#0000ff & {\rm \small \color{#0000ff}{Purest~blue}} & \#ffff00 & {\rm \small \color{#ffff00}{Purest~yellow}} & \#00ffff & {\rm \small \color{#00ffff}{Purest~cyan}}\\\hline \#0000ee & {\rm \small \color{#0000ee}{Darker~blue}} & \#eeee00 & {\rm \small \color{#eeee00}{Darker~yellow}} & \#00eeee & {\rm \small \color{#00eeee}{Darker~cyan}}\\\hline \#0000dd & {\rm \small \color{#0000dd}{Darker~blue}} & \#dddd00 & {\rm \small \color{#dddd00}{Darker~yellow}} & \#00dddd & {\rm \small \color{#00dddd}{Darker~cyan}}\\\hline \#0000cc & {\rm \small \color{#0000cc}{Darker~blue}} & \#cccc00 & {\rm \small \color{#cccc00}{Darker~yellow}} & \#00cccc & {\rm \small \color{#00cccc}{Darker~cyan}}\\\hline \#0000bb & {\rm \small \color{#0000bb}{Darker~blue}} & \#bbbb00 & {\rm \small \color{#bbbb00}{Darker~yellow}} & \#00bbbb & {\rm \small \color{#00bbbb}{Darker~cyan}}\\\hline \#0000aa & {\rm \small \color{#0000aa}{Darker~blue}} & \#aaaa00 & {\rm \small \color{#aaaa00}{Darker~yellow}} & \#00aaaa & {\rm \small \color{#00aaaa}{Darker~cyan}}\\\hline \#000099 & {\rm \small \color{#000099}{Darker~blue}} & \#999900 & {\rm \small \color{#999900}{Darker~yellow}} & \#009999 & {\rm \small \color{#009999}{Darker~cyan}}\\\hline \#000088 & {\rm \small \color{#000088}{Darker~blue}} & \#888800 & {\rm \small \color{#888800}{Darker~yellow}} & \#008888 & {\rm \small \color{#008888}{Darker~cyan}}\\\hline \#000066 & {\rm \small \color{#000066}{Darker~blue}} & \#666600 & {\rm \small \color{#666600}{Darker~yellow}} & \#006666 & {\rm \small \color{#006666}{Darker~cyan}}\\\hline \#000044 & {\rm \small \color{#000044}{Darker~blue}} & \#444400 & {\rm \small \color{#444400}{Darker~yellow}} & \#004444 & {\rm \small \color{#004444}{Darker~cyan}}\\\hline \#000022 & {\rm \small \color{#000022}{Darker~blue}} & \#222200 & {\rm \small \color{#222200}{Darker~yellow}} & \#002222 & {\rm \small \color{#002222}{Darker~cyan}}\\\hline \#000000 & {\rm \small \color{#000000}{Black}} & \#000000 & {\rm \small \color{#000000}{Black}} & \#000000 & {\rm \small \color{#000000}{Black}} \\\hline \end{array}

There's also #ff00ff for pink if you'd like. You can also use the CMYK color mode, as xcolor supports it.

_________________________________________

If you want a vivid black line separating the contents of your posts, type #________ instead of ______. However, then you have to adjust the number of chars manually by typing them.

---

Is ___ while

_________________________________

is #_________________________________. My biggest remorse (and @Martin's greatest joy) is that \rule doesn't work in MathJax.

_________________________________________

Markdown already has backticks for code formatting. However, those are prone to failure in, say for example, arrays. The $\LaTeX$ environment for codez is verbatim. There is the verbatim command and the verbatim environment, but only the command works in MathJax: $\verb+Dis iz some codez: \verb|stuff| is the syntax+$

Answer 16

Operations

• $a$ plus $b$

  $$a + b$$

• $a$ minus $b$

  $$a - b$$

• $a$ plus or minus $b$

  $$a \pm b$$

• $a$ minus or plus $b$

  $$a \mp b$$

• $a$ multiplied by $b$, $a$ times $b$

  $$a \cdot b$$ $$a \times b$$ $$a\;b$$ $$ab$$

• $a$ divided by $b$

  $$\frac{a}{b}$$ $$a/b$$

• $a_1 + a_2 + \ldots + a_n$, sum of $a_1$, $a_2$, …, $a_n$

  $$\sum\limits_{i = 1}^n a_i$$

• $a_1 \cdot a_2 \cdot \ldots \cdot a_n$, product of $a_1$, $a_2$, …, $a_n$

  $$\prod\limits_{i = 1}^n a_i$$

• $a$ to the power $p$

  $$a^p$$

• $a$ to the power $1/2$, square root of $a$

  $$a^{1/2}$$ $$\sqrt a$$

• $a$ to the power $1/n$, $n$th root of $a$

  $$a^{1/n}$$ $$\sqrt[n]{a}$$

• mean value of $x$, arithmetic mean of $x$

  $$\overline x$$ $$\left\langle x \right\rangle$$

• absolute value of $a$, modulus of $a$, magnitude of $a$

  $$\left| a \right|$$

Answer 17

Hazard pictograms

a) Each image is resized to ‘small thumbnail’ (160 × 160) by appending the single character suffix ‘t’ to the end of the image id, and before the file extension.

---

b) Each image is resized to 160 × 160 using HTML.

(To better see the difference, use the zoom feature in your web browser.)

Answer 18

Functions

• functions

  $$f,g,h, \ldots $$

• value of function $f$ for argument $x$

  $$f(x)$$ $$f{\left( x \right)}$$

• limit of $f{\left( x \right)}$ as $x$ tends to $a$

  $$\lim _{x \to a} f{\left( x \right)}$$ $${\lim}_{x \to a}f{\left( x \right)}$$

• delta $f$, finite increment of $f$

  $$\Delta f$$

• derivative of $f$ with respect to $x$

  $$\frac{\mathrm df}{\mathrm dx}$$ $$\mathrm df/\mathrm dx$$ $$f'$$

• value of the derivative of $f$ for $x = a$

  $$\left( \frac{\mathrm df}{\mathrm dx} \right)_{x = a}$$ $$\left( \mathrm df/\mathrm dx \right)_{x = a}$$ $$f'{\left( a \right)}$$

• $n$th derivative of $f$ with respect to $x$

  $$\frac{\mathrm d^nf}{\mathrm dx^n}$$ $$\mathrm d^nf/\mathrm dx^n$$ $$f^{\left( n \right)}$$

• partial derivative of $f$ with respect to $x$

  $$\frac{\partial f}{\partial x}$$ $$\partial f/\partial x$$ $$\partial _xf$$

• total differential of $f$

  $$\mathrm df$$

• infinitesimal variation of $f$

  $$\phantom{\text{(not rendered correctly)}\qquad}\mathrm \delta f \qquad\color{red}{\text{(not rendered correctly)}}$$

• indefinite integral of $f$

  $$\int {f{\left( x \right)}}\, \mathrm dx$$

• definite integral of $f$ from $a$ to $b$

  $$\int\limits_a^b {f{\left( x \right)}\, \mathrm dx} $$

Answer 19

\newcommand{\md}[0]{\mathrm{d}} \frac{\md\hbar}{\md\pi}

$$\newcommand{\md}[0]{\mathrm{d}} \frac{\md\hbar}{\md\pi} = 0$$

\md U = \md q + \md w

$$\md U = \md q + \md w$$

Please don't murder me for not using the inexact differential sign.

\langle \psi_1 | \psi_2 \rangle Doesn't look good on my computer. (OS X issue)

$$\Large \langle \psi_1 | \psi_2 \rangle$$

\langle \psi_1 \lvert \psi_2 \rangle Better.

$$\Large \langle \psi_1 \lvert \psi_2 \rangle$$

\langle \psi_1 \lvert \frac{a}{b} \rvert \psi_2 \rangle But it fails here.

$$\Large \langle \psi_1 \lvert \frac{a}{b} \rvert \psi_2 \rangle$$

\left\langle {\psi_1 \left| \frac{a}{b} \right| \psi_2 \right\rangle This solves the problem.

$$\Large \left\langle \psi_1 \left| \frac{a}{b} \right| \psi_2 \right\rangle$$

\left\langle \psi_1 \left| \Omega \right| \psi_2 \right\rangle But this is rubbish. (OS X issue again)

$$\Large \left\langle \psi_1 \left| \Omega \right| \psi_2 \right\rangle$$

\Large \left\langle \frac{a}{b} \left| \vphantom{\frac{a}{b}} \Omega \right| \frac{a}{b} \right\rangle with vertical phantom $$\Large \left\langle \frac{a}{b} \left| \vphantom{\frac{a}{b}} \Omega \right| \frac{a}{b} \right\rangle$$

\Large \left\langle \frac{a}{b} \left| \Omega \right| \frac{a}{b} \right\rangle without vertical phantom $$\Large \left\langle \frac{a}{b} \left| \Omega \right| \frac{a}{b} \right\rangle$$

\left\langle \frac{a}{b} \middle| \frac{a}{b} \right\rangle $$\Large \left\langle \frac{a}{b} \middle| \frac{a}{b} \right\rangle$$

\left\langle \frac{a}{b} \middle| \Omega \middle| \frac{a}{b} \right\rangle

$$\Large \left\langle \frac{a}{b} \middle| \Omega \middle| \frac{a}{b} \right\rangle$$

Answer 20

Oh no! We ha̟ve br͔̹̖oke̾̏ͮͤn the lḁ͎̙̹͇͉̔̏̄̇w̍̋͒̄̉ͣs͇̱̎͒ͤ̓͆ͮ͘ ̉ͭ̇͏̫̤̣̘ ̵͋o̶̒͌̄ͦ̔͘͢f̶͛̊ͧ̔̓̓͐ͯ̚ chemistry and physics!

Answer 21

\begin{array}{|c|c|c|c|c|c|c|}\hline {\small \color{red}{\mathbf{Site~Name}}} & {\small \mathit{x} \downarrow} & {\small \mathbf{\color{blue}{Total~Questions^{\large *}}}} & {\small \mathbf{\color{green}{Total~Answers^{\large *}}}} & {\small \mathbf{\color{magenta}{Visits/day}}} & {\small \mathbf{\color{brown}{QPD}}} & {\small \mathbf{\color{orange}{Site~Age (months)}}} \\\hline {\small \rm \color{red}{\mathsf{MathOverflow}}} & {\small \rm 342} & {\small \rm \color{blue}{63,595}} & {\small \rm \color{green}{102,901}} & {\small \rm \color{magenta}{16,785}} & {\small \rm \color{brown}{36}} & {\small \rm \color{orange}{71}} \\ {\small \rm \color{red}{\mathsf{Webmasters}}} & {\small \rm 305} & {\small \rm \color{blue}{21,236}} & {\small \rm \color{green}{35,494}} & {\small \rm \color{magenta}{13,002}} & {\small \rm \color{brown}{12}} & {\small \rm \color{orange}{61}} \\ {\small \rm \color{red}{\mathsf{ELL}}} & {\small \rm 287} & {\small \rm \color{blue}{18,605}} & {\small \rm \color{green}{33,168}} & {\small \rm \color{magenta}{33,678}} & {\small \rm \color{brown}{34}} & {\small \rm \color{orange}{31}} \\ {\small \rm \color{red}{\mathsf{Travel}}} & {\small \rm 264} & {\small \rm \color{blue}{13,344}} & {\small \rm \color{green}{23,433}} & {\small \rm \color{magenta}{33,069}} & {\small \rm \color{brown}{22}} & {\small \rm \color{orange}{50}} \\ {\small \rm \color{red}{\mathsf{Drupal~Answers}}} & {\small \rm 237} & {\small \rm \color{blue}{53,354}} & {\small \rm \color{green}{68,669}} & {\small \rm \color{magenta}{28,534}} & {\small \rm \color{brown}{41}} & {\small \rm \color{orange}{53}} \\ {\small \rm \color{red}{\mathsf{Blender}}} & {\small \rm 184} & {\small \rm \color{blue}{11,243}} & {\small \rm \color{green}{12,881}} & {\small \rm \color{magenta}{11,514}} & {\small \rm \color{brown}{29}} & {\small \rm \color{orange}{27}} \\ {\small \rm \color{red}{\mathsf{DIY}}} & {\small \rm 65} & {\small \rm \color{blue}{18,378}} & {\small \rm \color{green}{32,603}} & {\small \rm \color{magenta}{83,334}} & {\small \rm \color{brown}{21}} & {\small \rm \color{orange}{61}} \\ {\small \rm \color{red}{\mathsf{Webapps}}} & {\small \rm 91} & {\small \rm \color{blue}{17,756}} & {\small \rm \color{green}{26,361}} & {\small \rm \color{magenta}{51,572}} & {\small \rm \color{brown}{12}} & {\small \rm \color{orange}{62}} \\ {\small \rm \color{red}{\mathsf{Seasoned~Advice}}} & {\small \rm 87} & {\small \rm \color{blue}{13,006}} & {\small \rm \color{green}{33,294}} & {\small \rm \color{magenta}{93,182}} & {\small \rm \color{brown}{8.5}} & {\small \rm \color{orange}{61}} \\\hline \end{array}

Answer 22

$J_!^{8^\textrm{'}}(P')^{4^{'}}Y^4$ ffffffff

Here's a link

$\begin{bmatrix}O & I\\N & R & R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& N & R & R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R& R\end{bmatrix}$

Answer 23

The Tag Test

\begin{array}{|c|l|c|c|c|}\hline \# & {\small \bf Questions} & {\small \rm \color{green}{Yes}} & {\small \rm \color{#999999}{Partially}} & {\small \rm \color{red}{No}} \\\hline \hline 1&\small\text{Does 'experts on X' make sense?} & & & \\\hline 2&\small\text{Does 'I'm studying X' make sense?} & & & \\\hline 3&\small\text{Would you leave and not retag a question with only X as its tag?}~~~ & & & \\\hline 4&\small\text{Will 'because it's related to X' be the only reason a question is} \\[0pt] &\small\text{ tagged with X?}\,^1~~~~ & & & \\\hline 5&\small\text{Does X have a universally unambiguous meaning?} & & & \\\hline 6&\small\text{Will X not be misinterpreted, just judging by its name?} & & & \\\hline 7&\small\text{Are there many (>15) but not too many}\,^2 \small\text{ questions on the site} \\[0pt] &\small\text{ with the search keyword "X"?}\\\hline 8&\small\text{Will people search using X to find questions to answer?}\\\hline 9&\small\text{Without any personal feelings toward X, will people add it to} \\[0pt] &\small\text{their 'ignored' or 'favorite' tags?} \\\hline 10&\small\text{Can the questions to which X can be applied have other tags} \\[0pt] & \small\text{ reasonably applied as well?}\\\hline\end{array}

Answer 24

Space: the final frontier.

Comparison of space characters

$\text{abcdefghijklmnopqrstuvwxyz}$ (normal text without spaces)
$\mathrm{abcdefghijklmnopqrstuvwxyz}$ ab (no space)
$\mathrm{a{\kern 1pt}b{\kern 1pt}c{\kern 1pt}d{\kern 1pt}e{\kern 1pt}f{\kern 1pt}g{\kern 1pt}h{\kern 1pt}i{\kern 1pt}j{\kern 1pt}k{\kern 1pt}l{\kern 1pt}m{\kern 1pt}n{\kern 1pt}o{\kern 1pt}p{\kern 1pt}q{\kern 1pt}r{\kern 1pt}s{\kern 1pt}t{\kern 1pt}u{\kern 1pt}v{\kern 1pt}w{\kern 1pt}x{\kern 1pt}y{\kern 1pt}z}$ a{\kern 1pt}b (1 pt)
$\mathrm{a\,b\,c\,d\,e\,f\,g\,h\,i\,j\,k\,l\,m\,n\,o\,p\,q\,r\,s\,t\,u\,v\,w\,x\,y\,z}$ a\,b (thin space) $\mathrm{a\:b\:c\:d\:e\:f\:g\:h\:i\:j\:k\:l\:m\:n\:o\:p\:q\:r\:s\:t\:u\:v\:w\:x\:y\:z}$ a\:b (medium space)
$\mathrm{a\>b\>c\>d\>e\>f\>g\>h\>i\>j\>k\>l\>m\>n\>o\>p\>q\>r\>s\>t\>u\>v\>w\>x\>y\>z}$ a\>b
$\text{a b c d e f g h i j k l m n o p q r s t u v w x y z}$ a b (normal text) $\mathrm{a\ b\ c\ d\ e\ f\ g\ h\ i\ j\ k\ l\ m\ n\ o\ p\ q\ r\ s\ t\ u\ v\ w\ x\ y\ z}$ a\ b (control space)
$\mathrm{a~b~c~d~e~f~g~h~i~j~k~l~m~n~o~p~q~r~s~t~u~v~w~x~y~z}$ a~b (non-breaking space)
$\mathrm{a\;b\;c\;d\;e\;f\;g\;h\;i\;j\;k\;l\;m\;n\;o\;p\;q\;r\;s\;t\;u\;v\;w\;x\;y\;z}$ a\;b (thick space)
$\mathrm{a\enspace b\enspace c\enspace d\enspace e\enspace f\enspace g\enspace h\enspace i\enspace j\enspace k\enspace l\enspace m\enspace n\enspace o\enspace p\enspace q\enspace r\enspace s\enspace t\enspace u\enspace v\enspace w\enspace x\enspace y\enspace z}$ a\enspace b (en space)
$\mathrm{a\quad b\quad c\quad d\quad e\quad f\quad g\quad h\quad i\quad j\quad k\quad l\quad m\quad n\quad o\quad p\quad q\quad r\quad s\quad t\quad u}$ a\quad b (em space)
$\mathrm{a\qquad b\qquad c\qquad d\qquad e\qquad f\qquad g\qquad h\qquad i\qquad j\qquad k\qquad l\qquad m}$ a\qquad b (two quads)

  

Application

In math mode, MathJax ignores the spaces you type and puts in the spacing that it thinks is best. MathJax formats expressions the way it is common in mathematics texts. However, the printing rules for signs and symbols used in the natural sciences and technology require additional spaces (in particular, between the numerical value and the unit symbol). In math mode, use a\ b or a~b if you want the equivalent of space in normal text, e.g. M=46.068\ \mathrm{g\ mol^{-1}}:

$$M=46.068\ \mathrm{g\ mol^{-1}}$$

In integrals, MathJax cannot automatically enter a space of the correct size before the differential in the integrand. Therefore, manually insert a thin space \,, e.g. \int\limits_a^bx\,\mathrm dx: $$\int\limits_a^bx\,\mathrm dx$$

To facilitate the reading of numbers with many digits, these may be separated into groups of three, counting from the decimal sign towards the left and the right. Where such separation into groups of three is used, the groups shall be separated by a thin space a\,b and not by a point or a comma or by any other means, e.g. c_0=299\,792\,458\ \mathrm{m/s}: $$c_0=299\,792\,458\ \mathrm{m/s}$$

---

$\pu{1 ms-1}$ $\pu{1 ms-1}$ "per millisecond"
$1\ \mathrm{ms^{-1}}$ $1\ \mathrm{ms^{-1}}$ "per millisecond"
$\pu{1 m s-1}$ $\pu{1 m s-1} "metre per second", but the space is too small
$1\ \mathrm{m\ s^{-1}}$ $1\ \mathrm{m\ s^{-1}}$ "metre per second", okay
$1~\mathrm{m~s^{-1}}$ $1~\mathrm{m~s^{-1}}$ "metre per second", okay

Answer 25

Exponential and logarithmic functions

• base of natural logarithm

  $$\mathrm e$$

• $a$ to the power of $x$, exponential function to the base $a$ of argument $x$

  $$a^x$$

• $\mathrm e$ to the power of $x$, exponential function to the base $\mathrm e$ of argument $x$

  $$\mathrm e^x$$ $$\exp x$$

• logarithm to the base $a$ of argument $x$

  $$\log _a x$$ $\log x$ is used when the base does not need to be specified.

• natural logarithm of $x$

  $$\ln x$$ $\ln x = \log _\mathrm e x$

• decimal logarithm of $x$, common logarithm of $x$

  $$\lg x$$ $\lg x = \log _{10} x$

Answer 26

Operators

• $\hat{x}$ is the operator meaning $x$ (location)
• $\hat{p}$ (impuls) $\hat{p} = - i \hbar \frac{\partial}{\partial x}$

Operators and observables

$$\hat O f(x) = o \cdot f(x)$$ (Ô being the operator, o the observable)

Kinetic energy

$$E_{\mathrm{kin}} = \frac{1}{2} m v^2$$ $$p = m v$$ $$E_{\mathrm{kin}} = \frac{p^2}{2m}$$

Schrödinger equation

$$\hat H \Psi = E \Psi$$

With $\hat H = \hat T$ (all energy being kinetic energy) we get: $$\hat T \Psi = E_{\mathrm{kin}} \Psi$$ $$\frac{\hat p^2}{2m} \Psi = E_{\mathrm{kin}} \Psi$$ $$- \frac{\hbar ^2}{2m}\frac{\partial^2}{(\partial x)^2} \Psi = E_{\mathrm{kin}} \Psi$$

$$\Psi = \sqrt{\frac{2}{L}} \sin \left (\frac{n \pi x}{L}\right )$$

Answer 27

Line spacing

Normal line spacing:

$$\begin{align} \frac{Q_1}{Q_2} &= \frac{ \left\{ Q_1 \right\} \cdot \left[ Q_1 \right] }{ \left\{ Q_2 \right\} \cdot \left[ Q_2 \right] } \\ &= \frac{ \left\{ Q_1 \right\} }{ \left\{ Q_2 \right\} } \cdot \frac{ \left[ Q_1 \right] }{ \left[ Q_2 \right] } \end{align}$$

Additional vertical space:

$$\begin{align} \frac{Q_1}{Q_2} &= \frac{ \left\{ Q_1 \right\} \cdot \left[ Q_1 \right] }{ \left\{ Q_2 \right\} \cdot \left[ Q_2 \right] } \\[6pt] &= \frac{ \left\{ Q_1 \right\} }{ \left\{ Q_2 \right\} } \cdot \frac{ \left[ Q_1 \right] }{ \left[ Q_2 \right] } \end{align}$$

Answer 28

Exponents (150)

$x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$