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Contributing to BookOfProofs is easy - thanks to cool open source software!

Easy Posts With a Simple Text Markup

This site deploys a simple text markup found and used under conditions stated at https://raw.githubusercontent.com/netcarver/textile/2.5/classTextile.php,where you can also find exhaustive examples of syntax and usage. Here, we provide only some demo examples:

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Use h[1-6]. to create headers.

h1. My Header¶
h2. My Header¶
h3. My Header¶

Result:

My Header

My Header

My Header

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Creation of tables is very simple using | to indicate columns.

|_. heading one|_. heading two|
|<. left|>. right|
|^. top|<>{width:250px}. This is a 250px cell with a justified text inside.|
|~. bottom|=. This text will be centered. |
heading one heading two
left right
top This is a 250px cell with a justified text inside.
bottom This text will be centered.

It is also possible to span across columns and rows like this (shown in a table with border):

Markdown:

|\2=. this cell spans two columns|
|=. first column|=. second column|
|/3=. this row spans 3 rows|=. a|
|=. b|
|=. c|

Result:

this cell spans two columns
first column second column
this row spans 3 rows a
b
c
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Create external links in your text using quotation marks ".

Markdown:

"This is my external link":http://en.wikipedia.org/

Result:

This is my external link

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To create footnotes use [1-100], to actually type them use fn1. Footnote..., separated by empty lines, for instance:

Markdown:

p. This is a text with a footnote reference[1].
An this will create another reference[2].

p. Here comes another paragraph.

fn1. This is the first footnote
   ← empty line
fn2. This is the second footnoted.

This is a text with a footnote reference1.
An this will create another reference2.

Here comes another paragraph.

1 This is the first footnote

2 This is the second footnoted.

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Using exclamation marks !, you can include scaled images in your text and link to them:

Markdown:

!{width:250px}https://www.bookofproofs.org/graphics/examples/digraph1.gif!

Result:

Markdown:

!{width:350px}https://www.bookofproofs.org/graphics/examples/digraph1.gif!

Result:

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Create internal links in your text using quotation marks and the "dd"-notation ("drill-down" open book notation) ".

Markdown:

My internal link to "natural numbers":https://www.bookofproofs.org/branches/?dd=103

Result:

My internal link to natural numbers

Markdown:

My internal link to "Niels Henrik Abel":https://www.bookofproofs.org/history/?dd=3576

Result:

My internal link to Niels Henrik Abel

Close

Create internal links in your text using quotation marks and the "dd"-notation ("drill-down" open book notation) ".

My internal link to "natural numbers":https://www.bookofproofs.org/branches/natural-numbers/

Result:

My internal link to natural numbers

My internal link to "Niels Henrik Abel":https://www.bookofproofs.org/history/niels-henrik-abel/

Result:

My internal link to Niels Henrik Abel

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Use p. Text to create paragraphs.

p. This is a paragraph¶
p. And here begins a new pararagraph...¶

Result:

This is a paragraph.

And here begins a new pararagraph. Lorem ipsum dolor sit amet, ea dolore vivendum nec, sit at facer suscipit, sea affert vivendo maluisset no.

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Use bq. Text to quote.

p. This is a quotation:¶

bq. "Veni, vidi, vici"¶
Julius Caesar (100–44 BC).¶

Result:

This is a quotation:

“Veni, vidi, vici”
Julius Caesar (100–44 BC).

Close

Create lists using # for enumerations, * for itemizations, and - =: := for Redcloth-style definition lists.

Markdown:

# First Level
## Second Level
### Third Level

Result:

  1. First Level
    1. Second Level
      1. Third Level

Markdown:

* First Level
** Second Level
*** Third Level

Result:

  • First Level
    • Second Level
      • Third Level

Markdown:

- Term1 := Definition1
- Term2 := Extended
definition =:

Result:

Term1
Definition1
Term2
Extended
definition
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You can use inline modifiers to change the appearance of your text.

Markdown:

This text is _emphasized_.
This text is __italic__.
This text is *strong*.
This text is **bold**.
This text is ??cited??
This text is -deleted-.
This text is +inserted+.
This text is in ^superscript^.
This text is in ~subscript~.
This text is in @computer system script@.
%(red)This text is red.%
%(blue)This text is blue.%
%(green)This text is green.%
%(gray)This text is gray.%
%(w3-amber)This text is in one of the many w3-colors (see w3schools w3.css)%
==This text is not formated at all.==

Result:

This text is emphasized.
This text is italic.
This text is strong.
This text is bold.
This text is cited
This text is deleted.
This text is inserted.
This text is in superscript.
This text is in subscript.
This text is in computer system script.
This text is red.
This text is blue.
This text is green.
This text is gray.
This text is in one of the many w3-colors (see w3schools w3.css)
This text is not formated at all.


Beautiful Maths with MathJax

Mathjax is a powerful, open-source display engine for mathematics using client-side javascript in your browser.You can find more information at the MathJax homepage.If you are looking for an exhaustive list of MathJax syntax and the corresponding typesetting in action, you might visit http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm.Here, we provide only some formatting examples.

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Type mathematic formulae using \[...\] or type them inline using \(...\).

Mathjax:

p. The Cauchy-Schwarz Inequality states that
\[
\left( \sum_{k=1}^n a_k b_k \right)^{2} \leq
 \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]

p. Einstein's famous equation is \(E=mc^2\).

Result:

The Cauchy-Schwarz Inequality states that
\[
\left( \sum_{k=1}^n a_k b_k \right)^{2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]

Einstein’s famous equation is \(E=mc^2\).

Close

Superscripting and Subscripting

\(x^{2y}\)

Mathjax:

\(x^{2y}\)

Result:

\(x^{2y}\)

Mathjax:

\(x^{y^{2}}\)

Result:

\(x^{y^{2}}\)

Mathjax:

\(x_{1}^{a_{2}}\)

Result:

\(x_{1}^{a_{2}}\)

Fractions and Squares

Multiplying with \(\sqrt[n]{2}\) results in \( (m+n)/n\).

Mathjax:

Multiplying with
 \(\sqrt[n]{2}\)
 results in \( (m+n)/n\).

Result:

Result:

Multiplying with \(\sqrt[n]{2}\) results in \( (m+n)/n\).

Mathjax:

\frac{-b\pm
\sqrt{b^2-4ac}}{2a}

Result:

\(\frac{-b\pm
\sqrt{b^2-4ac}}{2a}\)

Mathjax:

\frac{x+y}
{1+\frac{y}{z+1}}

Result:

\(\frac{x+y}
{1+\frac{y}{z+1}}\)

Matrix and Ellipsis

\(x_{1},\ldots,x_{n}\)

Mathjax:

x_{1},\ldots,x_{n}

Result:

\(x_{1},\ldots,x_{n}\)

Mathjax:

x_{1},\cdots,x_{n}

Result:

\(x_{1},\cdots,x_{n}\)

Mathjax:

\left(\begin{array}{ccc}
x_{11}&\cdots&x_{1n}\\
\vdots&\ddots&\vdots\\
x_{n1}&\cdots&x_{nn}
\end{array}\right)

Result:

\(\left(\begin{array}{ccc}
x_{11}&\cdots&x_{1n}\\
\vdots&\ddots&\vdots\\
x_{n1}&\cdots&x_{nn}
\end{array}\right)\)

Close

Greek letters

\(\) \(\) \(\) \(\)
 \alpha 
\( \alpha \)
 \beta 
\( \beta \)
 \gamma,\Gamma 
\( \gamma,\Gamma \)
 \delta,\Delta 
\( \delta,\Delta \)
 \epsilon 
\( \epsilon \)
 \varepsilon 
\( \varepsilon \)
 \zeta 
\( \zeta \)
 ta 
\( ta \)
 \theta,\Theta 
\( \theta,\Theta \)
 \vartheta 
\( \vartheta \)
 \iota 
\( \iota \)
 \kappa 
\( \kappa \)
 \lambda,\Lambda 
\( \lambda,\Lambda \)
 \mu 
\( \mu \)
 \nu 
\( \nu \)
 \xi,\Xi 
\( \xi,\Xi \)
 o 
\( o \)
 \pi,\Pi 
\( \pi,\Pi \)
 \varpi 
\( \varpi \)
 \rho 
\( \rho \)
 \varrho 
\( \varrho \)
 \sigma,\Sigma 
\( \sigma,\Sigma \)
 \varsigma 
\( \varsigma \)
 \tau 
\( \tau \)
 \upsilon,\Upsilon 
\( \upsilon,\Upsilon \)
 \phi,\Phi 
\( \phi,\Phi \)
 \varphi 
\( \varphi \)
 \chi 
\( \chi \)
 \psi,\Psi 
\( \psi,\Psi \)
 \omega,\Omega\ 
\( \omega,\Omega\ \)
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Relations

 < 
('space > space') \( < \)
 > 
('space > space') \( > \)
\le
\(\le\)
\geq
\(\geq\)
\in
\(\in\)
\notin
\(\notin\)
\ni
\(\ni\)
\propto
\(\propto\)
=
\(=\)
\neq
\(\neq\)
\simeq
\(\simeq\)
\sim
\(\sim\)
\subset
\(\subset\)
\subseteq
\(\subseteq\)
\supset
\(\supset\)
\supseteq
\(\supseteq\)
\ll
\(\ll\)
\gg
\(\gg\)
\prec
\(\prec\)
\succ
\(\succ\)
\vdash
\(\vdash\)
\dashv
\(\dashv\)
\perp
\(\perp\)
\mid
\(\mid\)
\parallel
\(\parallel\)
\equiv
\(\equiv\)
\asymp
\(\asymp\)
\cong
\(\cong\)
\sqsubseteq
\(\sqsubseteq\)
\sqsupseteq
\(\sqsupseteq\)
\doteq
\(\doteq\)
\models
\(\models\)
\preceq
\(\preceq\)
\succeq
\(\succeq\)
\smile
\(\smile\)
\frown
\(\frown\)
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Arrows

 \leftarrow 
\( \leftarrow \)
 \rightarrow 
\( \rightarrow \)
 \longleftarrow 
\( \longleftarrow \)
 \longrightarrow 
\( \longrightarrow \)
 \Leftarrow 
\( \Leftarrow \)
 \Rightarrow 
\( \Rightarrow \)
 \Longleftarrow 
\( \Longleftarrow \)
 \Longrightarrow 
\( \Longrightarrow \)
 \Leftrightarrow 
\( \Leftrightarrow \)
 \leftrightarrow 
\( \leftrightarrow \)
 \Longleftrightarrow 
\( \Longleftrightarrow \)
 \longleftrightarrow 
\( \longleftrightarrow \)
 \uparrow 
\( \uparrow \)
 \Uparrow 
\( \Uparrow \)
 \downarrow 
\( \downarrow \)
 \Downarrow 
\( \Downarrow \)
 \nearrow 
\( \nearrow \)
 \searrow 
\( \searrow \)
 \nwarrow 
\( \nwarrow \)
 \swarrow 
\( \swarrow \)
 \mapsto 
\( \mapsto \)
 \longmapsto 
\( \longmapsto \)
 \leadsto 
\( \leadsto \)
 \rightleftharpoons 
\( \rightleftharpoons \)
 \leftharpoonup 
\( \leftharpoonup \)
 \rightharpoonup 
\( \rightharpoonup \)
 \leftharpoondown 
\( \leftharpoondown \)
 \rightharpoondown 
\( \rightharpoondown \)
 \hookleftarrow 
\( \hookleftarrow \)
 \hookrightarrow 
\( \hookrightarrow \)
 \updownarrow 
\( \updownarrow \)
 \Updownarrow 
\( \Updownarrow \)
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Operators and other Symbols

 + 
\( + \)
 - 
\( - \)
 \cdot 
\( \cdot \)
 \div 
\( \div \)
 \pm 
\( \pm \)
 \mp 
\( \mp \)
 \times 
\( \times \)
 \odot 
\( \odot \)
 \oplus 
\( \oplus \)
 \ominus 
\( \ominus \)
 \otimes 
\( \otimes \)
 \oslash 
\( \oslash \)
 \bullet 
\( \bullet \)
 \lfloor x \rfloor 
\( \lfloor x \rfloor \)
 \lceil x \rceil 
\( \lceil x \rceil \)
 \ast 
\( \ast \)
 \diamond 
\( \diamond \)
 \circ 
\( \circ \)
 \dagger 
\( \dagger \)
 \ddagger 
\( \ddagger \)
 \cap 
\( \cap \)
 \cup 
\( \cup \)
 \sqcap 
\( \sqcap \)
 \sqcup 
\( \sqcup \)
 \vee 
\( \vee \)
 \wedge 
\( \wedge \)
 \bigtriangleup 
\( \bigtriangleup \)
 \bigtriangledown 
\( \bigtriangledown \)
 \triangleleft 
\( \triangleleft \)
 \triangleright 
\( \triangleright \)
 \triangle
\( \triangle\)
 \Box 
\( \Box \)
 \lhd 
\( \lhd \)
 \rhd 
\( \rhd \)
 \wr 
\( \wr \)
 \amalg 
\( \amalg \)
 \uplus 
\( \uplus \)
 \nabla 
\( \nabla \)
 \| 
\( \| \)
 \surd 
\( \surd \)
 \setminus 
\( \setminus \)
 \emptyset 
\( \emptyset \)
 \top 
\( \top \)
 \bot 
\( \bot \)
 \prime 
\( \prime \)
 \partial 
\( \partial \)
 \forall 
\( \forall \)
 \exists 
\( \exists \)
 \neg 
\( \neg \)
 \backslash 
\( \backslash \)
 \angle 
\( \angle \)
 \infty 
\( \infty \)
 \flat 
\( \flat \)
 \natural 
\( \natural \)
 \sharp 
\( \sharp \)
 \star 
\( \star \)
 \clubsuit 
\( \clubsuit \)
 \diamondsuit 
\( \diamondsuit \)
 \heartsuit 
\( \heartsuit \)
 \spadesuit 
\( \spadesuit \)
 \aleph 
\( \aleph \)
 \hbar 
\( \hbar \)
 \imath 
\( \imath \)
 \jmath 
\( \jmath \)
 ll 
\( ll \)
 \wp 
\( \wp \)
 \Re 
\( \Re \)
 \Im 
\( \Im \)
 \mho 
\( \mho \)
 \unlhd 
\( \unlhd \)
 \unrhd 
\( \unrhd \)
 \Join 
\( \Join \)
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Big Operators and Symbols

 \sum 
\( \sum \)
 \prod 
\( \prod \)
 \coprod 
\( \coprod \)
 \bigsqcup 
\( \bigsqcup \)
 \int 
\( \int \)
 \iint 
\( \iint \)
 \iiint 
\( \iiint \)
 \iiiint 
\( \iiiint \)
 \oint 
\( \oint \)
 \oint\oint 
\( \oint\oint \)
 \bigcap 
\( \bigcap \)
 \bigcup 
\( \bigcup \)
 \bigoplus 
\( \bigoplus \)
 \biguplus 
\( \biguplus \)
 \bigodot 
\( \bigodot \)
 \bigotimes 
\( \bigotimes \)
 \bigvee 
\( \bigvee \)
 \bigwedge 
\( \bigwedge \)
 \Diamond 
\( \Diamond \)
 \bigcirc 
\( \bigcirc \)

Other Acknowledgements

To improve the user experience, the site uses the great open-source libraries of jquery mobile, smarty, JSXGraph,and Sagecell. We also thank Pixabay and its artists for beautiful pictures used on our site.


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