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General remarks on editing

You should feel welcome to contribute, even if you think what you write doesn't match the 'house style'.

In that case, this page is more to explain the meaning behind any minor changes that may be applied to your work after it has been submitted.

Over the course of prolonged contribution, it is considered both polite and very desirable that contributors put effort in mastering and adhering to house style, which is located at Help:House Style.

Should there be any questions, Help:Questions is the place to raise issues.

Page Editing

The purpose of this section is to describe the general structure that the various sections most used on $\mathsf{Pr} \infty \mathsf{fWiki}$ are to adhere to. While this naturally intersects with house style at some points, an attempt is made to separate the global editing instructions and section-specific instructions.

This reference provides the general outline on creating pages and instructions for specific sections; for the rest, see Help:House Style. Furthermore, this page does not dwell on details pertaining to the MediaWiki architecture; the reference for such things is Help:Wiki Editing.

Creating a Page

In general, pay attention to the fact that page names are case sensitive.

Pages can be created in several different ways. Before creating a page, please put some effort in ensuring that the anticipated content is not already up somewhere else on $\mathsf{Pr} \infty \mathsf{fWiki}$. This does also apply when following a red link; after all, the page in question may simply have a (slightly) different name.

By Searching

First, search for the page name which you would like to create. If this page has not already been created then you will see something that looks like this:

There is no page titled "Proof Name". You can create this page.

Clicking on create this page will open the page editing window.

Direct URL

If you know for sure that the proof is not on the site, then simply type that name into the URL. For example, if you wanted to prove the Riemann Hypothesis, you would type: Hypothesis

If this page does not exist then, you will get a single line saying:

There is currently no text in this page, you can search for this page title in other pages or edit this page.

Clicking edit this page will open the editing page where you can edit the page.

Page Naming

For all types of pages, major words in the title of the page should be capitalized. For example: Subring Generated by Unity of Ring with Unity. It is also generally better not to start a page name with "A" or "The", as this makes it significantly harder to find pages alphabetically in their categories. For example: Pythagorean Theorem, not The Pythagorean Theorem.

So as to promote consistency, be informed that in particular, the words 'iff', 'implies', and 'under' are not considered to be "major", and so are ought to be used in their lowercase form when naming a page.

Naming Proofs

It is not necessary to begin the name with "Proof of ...", and this should be avoided. Since $\mathsf{Pr} \infty \mathsf{fWiki}$ is a collection of proofs, it is assumed that each page is going to be a proof of something. This also makes searching for articles much easier.

If the name of a page contains mathematical statements, the following formatting practices should be adhered to:

  • Put no spaces between numbers/elements that are added, subtracted, divided, or multiplied together.
Eg: (1+2)x3.
  • Do, however, put spaces between elements that are put into equality or inequality with one another, and please use != to signify inequality.
Eg: 1 = 3/3 != 3/4.

Naming Other Pages

When you would like to create a page for a definition, all you have to do different from naming a proof is to add Definition: in front of the name. So for example if you wanted to create a page for the definition of calculus you would name the page:


Also, after you create the page, be sure to add the definition to the appropriate "Definitions" categories (see Category:Definitions).

The same method that is used for Definitions is also used to name and categorize axiom and symbols pages. Simply substitute Symbol or Axiom for Definition: in the page name and, mutatis mutandis, in the category name.

Disallowed Characters

The following characters should not be used in page names:

# < > [ ] | { } * & $ @


The technique of disambiguation serves to resolve conflicts arising from multiple concepts or results having the same name.

It is generally to be used only if the concepts are unrelated; for theorems, disambiguation is always required.

To disambiguate a page, first ensure that the page (if it exists) previously on the place the disambiguation will be is given an appropriate new title.

Take care to update any links to the page (which can be viewed using the "What links here" option in the menu, under Toolbox) to the new page before installing the disambiguation. If this is an involved and long-winded task, an appropriate invocation of Template:WIP may be added to the disambiguation page to signify the task is still unfinished.

When this is all taken care of, replace the content of the page with:

* [[Disambiguated Page 1]]
* [[Disambiguated Page 2]]
* Etc.

It is understood that when the disambiguation resides in the Definition namespace, it is to be placed in Category:Definitions. Disambiguations of theorems needn't be added to a category.

Each entry may feature a short line describing the particular page it links to, but this isn't required.

When the disambiguation is finished, it is a good idea to put an instance of the About template at the top of every page it disambiguates.

Instructions on how to use this template can be found by following the link above.

Multiple Names

Some mathematical concepts have several names, according to the sources you consult. Which of these names is used in $\mathsf{Pr} \infty \mathsf{fWiki}$ is largely a matter of happenstance.

However, if one of the names of a concept is for a particular mathematician, that name is to be used in preference.

An example of this is Definition:Chebyshev Distance, which is otherwise known as the Definition:Maximum Metric or the Definition:Chessboard Metric.

Writing Pages

Of course the most important part is to fill pages with actual content. On all pages (except for talk and user pages), the House Style applies.

Generally, pages follow this format:

== Theorem ==

State the theorem here.

== Proof ==

State the proof here.

== Also see ==

* List of (internal) links to closely related material.

== Sources ==

Add citations here.

[[Category:The Category]]

Below, various recurring sections on $\mathsf{Pr} \infty \mathsf{fWiki}$ pages and their particular rules are explained. All of these should have a type 2 heading.

The sections should be placed in the following order (with this exact capitalization):

  1. Definition / Theorem
  2. Proof
  3. Also known as
  4. Also defined as
  5. Also see
  6. Named for
  7. Historical Note
  8. Linguistic Note
  9. Technical Note
  10. Sources

and at the bottom of the page, categories should be added. See Help:Categories for documentation on categories.

Definitions and Theorems

These are in practice split into two parts (which is made visual by extra blank lines separating them).

Namely, first there is a series of lines, typically starting with "Let", introducing all names and concepts needed for stating the actual definition or theorem.

Then, separated by two blank lines, the definition or theorem itself is stated. Thus, we obtain the following structure (analogous for Theorems):

== Definition ==

Let ...
Let ...

Then '''what is to be defined''' is defined as ...

The concept that is to be defined is to be displayed in bold (i.e., with three apostrophes, ', on either side) throughout the page to make it stand out.


Besides adhering to house style, it is a good idea to separate different stages of the proof by subsections or whitespace. Other than that, rigour is the only real prerequisite for proofs.

If you would like other contributors to check your proof, please use the proofread template.

Also known as

Use this section when a concept or result is referred to in multiple ways; this is most commonly used for definitions.

All names should appear in bold. Should an alternative name coincide with the $\mathsf{Pr} \infty \mathsf{fWiki}$ name of something else, it is good to draw the reader's attention to this by including a link and a comment.

Also defined as

Use this section when a single name is used in the literature for multiple definitions. Typically, it is to be used mainly when these definitions are in the same field of mathematics. In other cases, a disambiguation is usually more appropriate. See Help:Disambiguation for instructions on that.

It is advisable to create a synthesis of this and the "Also known as" section. That is, to place "Also known as" sections on pages that are referred to in this section.

Also see

The "Also see" section is intended to contain references to closely related concepts and/or results. These are entered as a bulleted list:

== Also see ==

* [[Check This Out 1]]
* [[Check This Out 2]]
* Etc.

It is understood that definitions should be referenced in this section directly, without providing a reader view. This is to make it easy to see which entries are definitions and which are proofs.


* [[Definition:Increasing Sequence of Sets]]

is a correct entry.

In addition to the above, when a definition has an associated category, this category is to be referenced as well.

For example, Definition:Set Union refers to Category:Union. This is accomplished by the LinkToCategory template, entered as:

{{LinkToCategory|Union|set union}}

More documentation for this template can be found on its page: Template:LinkToCategory.

Source of Name

This section is exclusively created by the namedfor template.

It is entered as:

{{namedfor|Name of mathematician|cat = Surname of mathematician}}

where Surname of mathematician is actually the name of the mathematician's subcategory of Category:Named Theorems -- multiple notable mathematicians with identical surnames exist.

If some page is named for multiple mathematicians (e.g. Cayley-Hamilton Theorem) they should all be listed, via:

{{namedfor|Name 1|cat = Surname 1|name2 = Name 2|cat2 = Surname 2}}
{{namedfor|Name 1|cat = Surname 1|name2 = Name 2|cat2 = Surname 2|name3 = Name 3|cat3 = Surname 3}}

Historical Note

The Historical Note section is intended as a relatively free-form section in which any interesting information about the concept can be elaborated on.

If there is already a "Source of Name" section, then if what you want to say consists of a sentence or two, it may be better just to add it to directly after your invocation of the namedfor template. See Fermat's Little Theorem for a simple example. On the other hand, see Fermat's Christmas Theorem for an example of where the author has considered it appropriate to create a separate section.

If you have a great deal to say about the subject in question, then it is worth considering whether to write it as a separate transcluded page.

Indeed, if you have a strong interest and expertise in the history of mathematics and wish to impart that knowledge on this website, then it may be a worthwhile future task setting up a properly structured category for the history of mathematics, into which we may find it worthwhile to migrate, for example, our ProofWiki:Mathematicians space into.

This is one area of $\mathsf{Pr} \infty \mathsf{fWiki}$ whose evolution is in progress.

Linguistic Note

If a term being defined is not a common word in natural language, then it may be appropriate to give an indication of various linguistic characteristics of that word.

Examples of this are:

  1. Its pronunciation (for example: see Definition:Integer)
  2. Its plural form (for example: see Definition:Continuum (Topology)‎)
  3. Its etymology (for example: see Definition:Summand)

Boldface is used for all words which directly relate to the term being defined.

The pronunciation is given in simple, phonetic English, with syllables separated by hyphens.

Stressed syllables are indicated in italics, hence the rendering: syl-la-ble.

Note that the Linguistic Note section is not mandatory for any page; it is created only when there is a need.

It needs to be remembered that $\mathsf{Pr} \infty \mathsf{fWiki}$ is accessed by users worldwide, to whom English is not their first language, and may not be familiar with many aspects of mathematical language which may be taken for granted by a native English speaker.

Also note that if there are differences between UK and US English forms of the spelling, the pronunciation or the plural form of any term, then this is the section to document it.

Technical Note

On definitions pages, typically some notation is introduced.

When rendering this notation using $\LaTeX$ requires some involved trickery, the code for achieving this may be explained in a section named "Technical Note".

See Definition:Convergence in Measure for an example.


This section serves to list the sources backing up a certain page. They are to be listed first in chronological order, then alphabetically on the name of the (first) author.

For example (an excerpt of the Sources section of Definition:Set Union):

== Sources ==

* {{BookReference|Naive Set Theory|1960|Paul R. Halmos|prev=Union of Singleton|next=Union with Empty Set}}: $\S 4$: Unions and Intersections
* {{BookReference|Abstract Algebra|1964|W.E. Deskins|prev=Equality of Sets|next=Definition:Set Intersection}}: $\S 1.1$: Definition $1.2$
* {{BookReference|Point Set Topology|1964|Steven A. Gaal|prev=Definition:Set Union/General Definition|next=Union is Commutative}}: Introduction to Set Theory: $1$. Elementary Operations on Sets
* {{BookReference|Sets and Groups|1965|J.A. Green|prev=Empty Set Subset of All|next=Intersection Subset Union}}: $\S 1.4$
* {{BookReference|Modern Algebra|1965|Seth Warner|prev=Associative and Anticommutative|next=Definition:Set Intersection}}: $\S 3$

Because this section is of paramount importance for the reliability of $\mathsf{Pr} \infty \mathsf{fWiki}$, it and its constituents are discussed in detail on a dedicated page, Help:Sources.

Wiki Editing

The definitive reference on wiki editing is of course MediaWiki's own site, in particular the MediaWiki Help Pages.

The below gives an overview of the wiki functionality that is most frequently used on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Text styles

Text you would like to be bold should be enclosed in three single quotes. For example:

 '''Bold text''' 

creates: Bold text.

Italic font is produced with two single quotes, for example:

 ''Italic text'' 

creates: Italic text

To produce bold, italicised writing, use five consecutive single quotes:

 '''''Bold and italic text''''' 

creates: Bold and italic text.

Fixed width text:

 <code> Fixed width text</code> 

creates: Fixed width text

Note that while:

 <tt> Fixed width text </tt> 

produces the same result, the tt tag is known to be badly behaved in combination with MediaWiki, creating rendering issues.

Therefore, the code tag is to be used universally on $\mathsf{Pr} \infty \mathsf{fWiki}$ to generate fixed width text.

Line breaking

Breaking a line in the editor does not break a line in the displayed text. For example:

''I will continue this''
''on the next line''

displays as:

I will continue this on the next line.

To break a line, space the text with a single blank line:

''I will continue this''

''on the next line''

Sections and subsections

A section heading is produced by enclosing the desired title between two equals (=) signs. For example:

 == Definition == 

will produce a section entitled "Definition".

A subsection should be enclosed between three equals signs, for example:

 === Subsection === 

will produce a subsection within the section that it is located.

One can continue making sub-subsections etc. with four or more equals signs.

For documentation of the accepted house style regarding sections, see Help:House Style.

Inclined to move the below to referenced Help:House Style.

As a general rule on spacing, each section or subsection heading should be preceded by two blank lines and followed by a single blank line.

Each sentence should appear on a separate line, with a single blank line above and below. For example:

This line precedes the section.

== Section heading ==

Line one of the section.

Line two of the section.

Indenting and bullet points

To indent a sentence or equation, add a colon (:) at the start of the line. For example:

 :Indented material 

will produce:

Indented material

For a larger indent use two or more colons.

For example, it is required by house style that each displayed equation be preceded with a single colon.

To produce a list of bullet points, write each point on a line beginning with an asterisk (*). For example:

* Bullet point 1
* Bullet point 2


  • Bullet point 1
  • Bullet point 2

As a notable discrepancy in house style, the empty lines guideline does not apply to successive items of lists.

This is because doing so results in a slight spacing issue, as seen in:

* Bullet point 1
* Bullet point 2

* Bullet point 3

which renders as:

  • Bullet point 1
  • Bullet point 2
  • Bullet point 3

On $\mathsf{Pr} \infty \mathsf{fWiki}$, these lists are mainly used in the Also see and Sources sections.

Link to internal page

To link to another page on $\mathsf{Pr} \infty \mathsf{fWiki}$, you must enclose the page name in double square brackets.

For example, to link to Pythagoras's Theorem, you would type:

 [[Pythagoras's Theorem]] 

To change the text to say something different and still link to that page you need to use a pipe character (|).

For example to link here you would type:

 [[Pythagoras's Theorem|here]] 

To link to a particular section on a page, append a octothorpe (#) to the page name followed by the subsection.

For example, to link here you would type:

 [[Pythagoras's Theorem#The Classic Proof|here]] 

This means of reference is generally going out of fashion on $\mathsf{Pr} \infty \mathsf{fWiki}$ due to the advent of the transclusion method.

In the above example, it would be more correct to refer to the subpage containing the "Classic Proof", viz here:

 [[Pythagoras's Theorem/Classic Proof|here]] 

There may be instances though where its use will be continued, for example to link to particular sections of the main wiki talk page in discussions.

For more information on the house style stipulations regarding internal reference, see Help:House Style.

Redirecting a page

If a theorem or definition is commonly known by more than one name, rather than create two separate pages just one page should be created, and the second redirected to the first.

This should be done with the command:

 #Redirect [[Page Name]] 

For example, to redirect a page to Pythagoras's Theorem enter:

 #Redirect [[Pythagoras's Theorem]] 

See Help:Redirects for more information on redirecting pages and the associated house style.

Link to external page

Linking to an external page is almost the same as linking to an internal page.

You need to enclose the page name in square brackets, [].

To add text the link, you just have to add what you want to name the link inside the brackets.

For example:

 [ Google] 

would create a link that looked like this: Google


References can easily be created by enclose the reference inside a <ref></ref> tag in the area you would like referenced. Then near the end of your article include this: <references/> . This will be where the references are actually listed. For an example see the below:

According to scientists, the Sun is pretty big.[1] The Moon, however, is not so big.[2]


  1. E. Miller, The Sun, (New York: Academic Press, 2005), 23-5.
  2. R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 44-6.

The code for this:

According to scientists, the Sun is pretty big.<ref>E. Miller, The Sun, (New York: Academic Press, 2005), 23-5.</ref>
The Moon, however, is not so big.<ref>R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 44-6.</ref>


Typically, it is desirable to collect the references under a designated 'type-2' header named 'References', whose code is:

== References ==

This section is best placed directly above the "Sources" section. For more information on page structuring, see Help:Page Editing.


Transclusion is a MediaWiki feature that allows (part of) a page to be displayed verbatim on another.

Since the construct is rather involved, it is explained on its own page, Help:Transclusion.

The $\mathsf{Pr} \infty \mathsf{fWiki}$ extension

The $\mathsf{Pr} \infty \mathsf{fWiki}$ extension is an amendment of MediaWiki's code that enables certain site-specific constructs.

See Help:ProofWiki Extension for documentation on this feature.

$\LaTeX$ Editing

In general, contributors are assumed to be up to speed with some form of $\LaTeX$; a web search should be sufficient to find ample reference on how to get started with it, should you still need to.

The "External references" section below may also be consulted.

The $\LaTeX$ interpreter used on this site is brought to you by MathJax.

This produces an experience different from that produced by the MediaWiki interpreter which is (at time of writing) the one used by Wikipedia and other places.

It also has a subtly different syntax in places. Specific instances will be detailed where relevant.

$\LaTeX$ delimiters

To display an equation in line with some text, the equation should be enclosed in single dollar signs: $ ... $

Note that \( ... \) also works, but takes more effort to type and so is less recommended.

There may (but we hope not) still be some pages with <math> ... </math> in them. This is a holdover from when MediaWiki was the interpreter used for $\LaTeX$ commands. It still works in MathJax after a fashion but on transcluded pages, such enclosed $\LaTeX$ will not be converted to mathematical symbols.

If you see any, then feel free to change them to $ signs, as they should not be there.

No longer supported

The following $\LaTeX$ commands are not supported in MathJax, but may still be present in some pages. When found they need to be replaced.

For $\lor$: \or to be replaced by \lor
For $\land$: \and to be replaced by \land
For $\R$: \reals to be replaced by \R
For $\varnothing$: \O to be replaced by \varnothing
For $\exists$: \exist to be replaced by \exists
For $\operatorname{sgn}$: \sgn to be replaced by \operatorname{sgn}

For producing fixed width text in math mode: \texttt needs to be replaced by \mathtt.

If you find any more examples, add them here.

External references

It may not be exactly the same version of $\LaTeX$, but I always find this page helpful as a first, quick overview:

This is also a good reference page, pertaining to MediaWiki $\LaTeX$:

but be aware that not all commands are supported.

This is a link of all the currently supported commands available: