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At least two of the examples of `\underbrace`, were doubly nested. I think that it is easiest for people to learn about the `\underbrace` command by seeing two examples (1) an example in which only one `\underbrace` is used (2) an example in which the underbrances are nested.
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Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$$\overbrace{(n - 2) + (n - 1) + (n + 0) + (n + 1) + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$$\underbrace{(n - 2) + (n - 1) + (n + 0) + (n + 1) + (n + 2)}$

\underbrace: underbraces can be nested, like this: $\underbrace{(n - 2) + \underbrace{(n - 1) + \underbrace{(n + 0)} + (n + 1)} + (n + 2)}$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{level}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X \overset{a}{\underset{b}{\to}} Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{level}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X \overset{a}{\underset{b}{\to}} Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + (n - 1) + (n + 0) + (n + 1) + (n + 2)}$

\underbrace: $\underbrace{(n - 2) + (n - 1) + (n + 0) + (n + 1) + (n + 2)}$

\underbrace: underbraces can be nested, like this: $\underbrace{(n - 2) + \underbrace{(n - 1) + \underbrace{(n + 0)} + (n + 1)} + (n + 2)}$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{level}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X \overset{a}{\underset{b}{\to}} Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

underset
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Mike Pierce
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Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{belowlevel}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

Arc over points\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X \overset{a}{\underset{b}{\to}} Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{below}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{level}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

\underset{below}{level}: $\underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T}$

You can use these together too. You can type $X \overset{a}{\underset{b}{\to}} Y$ with X\overset{a}{\underset{b}{\to}}Y.

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Added arc over points
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Américo Tavares
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Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{below}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{below}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

Additional decorations

$\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}$

\overline: $\demo\overline A$

\underline: $\demo\underline B$

\widetilde: $\demo\widetilde C$

\widehat: $\demo\widehat D$

\fbox: $\demo\fbox {$E$}$

\underleftarrow: $\demo\underleftarrow{F}\qquad$ variant: \xleftarrow{}: $\xleftarrow{abc}$

\underrightarrow: $\demo\underrightarrow{G}\qquad$ variant: \xrightarrow{}: $\xrightarrow{abc}$

\underleftrightarrow: $\demo\underleftrightarrow{H}$

\overrightarrow $\demo\overrightarrow{AB}$

\overbrace: $\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$

\underbrace: $(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$

\overbrace and \underbrace accept a superscript or a subscript, respectively, to annotate the brace. For example, \underbrace{a\cdot a\cdots a}_{b\text{ times}} is $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$

Note: \varliminf: $\varliminf$ and \varlimsup:$\varlimsup$ have special symbol of their own.

Single character accents

\check: $\check{I}$

\acute: $\acute{J}$

\grave: $\grave{K}$

\vec: $\vec u\ \vec{AB}$ (c.f. \overrightarrow above)

\bar: $\bar z$

\hat: $\hat x$

\tilde: $\tilde x$

\dot \ddot \dddot: $\dot x,\ddot x,\dddot x$

\mathring: $\mathring A$

General stacking

If you cannot find your symbol remember that you can stack various symbols using

\overset{above}{below}: $\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}$

Arc over points

\overset{ \huge\frown}{PQ}: $\overset{ \huge\frown}{PQ}$ denotes the arc over points $P$ and $Q$ (As per comment of @Calvin Khor to @Paul Sinclair's question)

added \overrightarrow, common vector notation
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Calvin Khor
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correcting accidental deleting of \demo
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zwim
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Added some variants of arrows with text, single char accents, and general stacking section.
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zwim
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added 224 characters in body
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MJD
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Fixed \underrightarrow; Added \overbrace and \underbrace
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Added additional accents
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Américo Tavares
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typo.
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Guy
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put examples next to the commands that generate them
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MJD
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Américo Tavares
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Post Made Community Wiki by Américo Tavares