# Help:Page Structure

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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:

1. Definition / Theorem
2. Proof(s)
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

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:

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.

#### 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.