Help:Page Structure

The purpose of this page is to describe the general structure that the various sections most used on 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
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.

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:


 * Definitions
 * Multiple Definitions
 * Proofs
 * Multiple Proofs
 * Equivalence Proofs
 * Examples
 * Axioms

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.

Sections
Below, various recurring sections on 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

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.

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.

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

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:

where  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:

A similar technique is used for definitions.

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

and again for axioms:

The same extensions apply for multiple mathematicians.

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.