# Help:Page Editing

## Page Editing

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.

## Existing pages

If you are a new user, it is best to leave these alone at the beginning.

Editing of existing pages *is* allowed, but is restricted to the following situations.

- There is a mathematical error on the page
- You are putting the proof in house style
- A step in the proof is not explained in sufficient detail
- Other things are missing which should be added

*Do not make any other change to any proof.* If you cannot resist modifying an existing proof, copy and paste the proof (creating a section "Proof 2" for instance) and make your changes there.

## Creating a Page

After searching, you may conclude that the page you're looking for does not exist yet. There are several ways to create it.

### By Searching

Search for the page name which you would like to create. As you have found out by now, the page has not already been created. You will see something that looks like this:

**Create the page "Proof name" on this wiki!**

Clicking on **Proof name** will open the page editing window, and you can start writing.

### By following a red link

All you have to do is click the red link and start writing.

### By entering a 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:

http://www.proofwiki.org/wiki/Riemann 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, search the related logs, or create this page.

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

## Deleting a page

Don't do this. Only trusted users can delete pages in any event; but this website has a strict non-deletion policy. Hence, deletions on this website happen very rarely.

## Page Naming

Choosing a good page title is important for multiple reasons:

- It makes the page easier to search for.
- The title gives a first impression of what the page is about. A good title adds to the understanding.
- The title is what is used in links. It's always nice to know what a page is about before clicking the link.
- A descriptive title avoids name conflicts

Some pages are subject to specific naming conventions. See the corresponding help pages for instructions:

Page titles that do not meet the standards can be flagged for renaming.

## Tips to choose a good name

### Be specific

There's no such thing as being too specific! In particular, page names consisting of a single word should generally be avoided: you never know if there are other concepts in mathematics with the same name. That is:

- not Definition:Prime Ideal but Definition:Prime Ideal of Ring
- not Definition:Supremum or Definition:Supremum of Set but Definition:Supremum of Subset of Real Numbers

The word "of" comes in handy here.

In the same spirit, it is a good practice to always include at least one noun in the title. That is:

- not Definition:Differentiable but Definition:Differentiable Mapping
- not Definition:Simple but Definition:Simple Group

Note how the shorter page names are always disambiguation pages.

For theorems, the same philosophy applies:

### Redundant words

Page names should not be started with articles such as "A" or "The", as this makes it significantly harder to find pages alphabetically in their categories. For example: Pythagorean Theorem, not The Pythagorean Theorem.

Similarly, 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.

In general, the words "the", "a" or "an" are strongly discouraged in page names, as they make the name longer than necessary and rarely add clarity to the concept being defined. The main exception to this rule are for concepts split into subtypes named along the lines "of the $n$th kind" , for example: Definition:Elliptic Integral of the First Kind.

### Descriptiveness

A good page title describes the content accurately. Because theorems are linked to using their exact page title, when reading a proof it is useful when you can guess what a theorem is about without having to visit the page. In particular, if a theorem contains an equivalence proof, the title should makes this clear, by using "iff".

### Don't blindly trust literature

Books, thanks to their limited scope, can afford to use simplified terminology without running into ambiguity problems. At $\mathsf{Pr} \infty \mathsf{fWiki}$ we can not. Thus it is a good idea to check if there is a danger for name conflicts by doing some research. Alternatively, make the name overly specific.

As for theorems, books may call a theorem "Fundamental Property of Homomorphisms" or "Continuity Property". This does not mean that the theorem is everywhere known by that name. While at $\mathsf{Pr} \infty \mathsf{fWiki}$ we do prefer to use as a title the name of a theorem rather than a description of the result, we do so only if there is no ambiguity.

## Naming conventions

### Namespaces

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:

Definition:Calculus

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. See Help:Categories.

### Capitalizing

Page titles are **case-sensitive**. 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.
So as to promote consistency, be informed that in particular, the following words are not considered to be "major" and ought to be used in their lowercase form when naming a page:

- Prepositions, pronouns and conjunctions:
- and, around, as, between, by, for, from, if, iff, in, its, minus, no, not, of, on, or, over, plus, such that, that, the, then, to, under, with, with respect to, which, whose

- Short verbs, such as:
- are, can, cannot, does, equals, form, has, have, implies, is

These lists are not exhaustive.

Variables in formulas are not capitalized. See #Names with Formulas.

### Names with Formulas

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.
- Example:
`(1+2)x3`

- Example:
- Do, however, put spaces between elements that are put into equality or inequality with one another. Use
`!=`

to signify inequality.- Example:
`1 = 3/3 != 3/4`

- Example:
- Variables appearing in the formulas need not be capitalized.
- Example:
`Primitive of x squared over a x + b`

- Example:
- A page name is no place for $\LaTeX$ commands.

## Things named after a mathematician

A theorem that is named after a Mathematician gets a call of the **Namedfor template**. When done properly, the page is then automatically placed in a corresponding category in Named Theorems, which itself has to be created manually.

Similarly, for named definitions there is the **NamedforDef template**.

Disambiguation pages are treated in the same way. Note that theorem disambiguations do not otherwise get categories. See Help:Disambiguation.

A page whose name contains a word named after a Mathematician does not fall under this category. For example, not every theorem about Krull dimension needs a call of Namedfor.

## 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.

See also Help:Also known as.

## Special Characters

### Disallowed Characters

The following characters should not be used in page names:

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

### Accented Characters

A theorem named after someone gets this exact name, including accented characters.

For search convenience, a redirect can be set up. See Help:Redirects#Accented characters

## Page Structure

The purpose of this page 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.

## Introduction

On all pages (except for talk and user pages), the House Style applies.

This page gives the general structure that applies to all pages. Click on the links below for the more precise expected format, which depends on the type of page:

## General Format

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]]

## Sections

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:

- Definition / Theorem
- Proof(s)
- Also known as
- Also defined as
- Also see
- Named for
- Historical Note
- Linguistic Note
- Technical Note
- Sources

Other optional sections include:

and more, such as remarks, comments, notations, for which there are no written guidelines yet.

#### 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.

#### Proofs

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.

#### Notes (avoid)

Try to avoid having a general "Notes" section on a page you create or edit. Instead, try to put any remarks you want to add into one of the sections listed next.

#### Explanation

This section can be used to explain concepts, in particular on pages that give definitions or describe types of proofs. To give context, consider using an "Also see" section.

#### 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.

Thus:

* [[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:Set Union. This is accomplished by the LinkToCategory template, entered as:

{{LinkToCategory|Set 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}}

A similar technique is used for definitions.

If a definition is named for a particular mathematician, then the NamedforDef template is used:

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

and again for axioms:

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

The same extensions apply for multiple mathematicians.

#### 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 Two Squares 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 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:

- Its pronunciation (for example: see Definition:Integer)
- Its plural form (for example: see Definition:Continuum (Topology))
- 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.

#### Sources

This section serves to list the sources backing up a certain page. 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.

## Categories

At the very bottom of the page, **categories** have to be added. See Help:Categories for documentation.