# Help: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

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

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:

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:

not Uniqueness of Extension but Uniqueness of Analytic Continuation

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

## Special Characters

### Disallowed Characters

The following characters should not be used in page names:

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

If you find any more examples, add them here.

### New commands

New commands can be requested and discussed at Symbols:LaTeX Commands/ProofWiki Specific, transcluded here:

 $\AA$ $\quad:\quad$\AA $\qquad$that is: \mathcal A $\Add$ $\quad:\quad$\Add $\qquad$Addition as a Primitive Recursive Function‎ $\adj {\mathbf A}$ $\quad:\quad$\adj {\mathbf A} $\qquad$Adjugate Matrix $\arccot$ $\quad:\quad$\arccot $\qquad$Arccotangent $\arccsc$ $\quad:\quad$\arccsc $\qquad$Arccosecant $\arcsec$ $\quad:\quad$\arcsec $\qquad$Arcsecant $\Area$ $\quad:\quad$\Area $\qquad$Area of Plane Figure $\Arg z$ $\quad:\quad$\Arg z $\qquad$Principal Argument of Complex Number $\Aut {S}$ $\quad:\quad$\Aut {S} $\qquad$Automorphism Group $\BB$ $\quad:\quad$\BB $\qquad$that is: \mathcal B $\Bernoulli {p}$ $\quad:\quad$\Bernoulli {p} $\qquad$Bernoulli Distribution $\BetaDist {\alpha} {\beta}$ $\quad:\quad$\BetaDist {\alpha} {\beta} $\qquad$Beta Distribution $\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a}$ $\quad:\quad$\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a} $\qquad$Limits of Integration $\Binomial {n} {p}$ $\quad:\quad$\Binomial {n} {p} $\qquad$Binomial Distribution $\bsDelta$ $\quad:\quad$\bsDelta $\qquad$a vector '$\Delta$' $\bsone$ $\quad:\quad$\bsone $\qquad$vector of ones $\bst$ $\quad:\quad$\bst $\qquad$a vector 't' $\bsv$ $\quad:\quad$\bsv $\qquad$a vector 'v' $\bsw$ $\quad:\quad$\bsw $\qquad$a vector 'w' $\bsx$ $\quad:\quad$\bsx $\qquad$a vector 'x' $\bsy$ $\quad:\quad$\bsy $\qquad$a vector 'y' $\bsz$ $\quad:\quad$\bsz $\qquad$a vector 'z' $\bszero$ $\quad:\quad$\bszero $\qquad$vector of zeros $\map \Card {S}$ $\quad:\quad$\map \Card {S} $\qquad$Cardinality $\card {S}$ $\quad:\quad$\card {S} $\qquad$Cardinality $\Cauchy {x_0} {\gamma}$ $\quad:\quad$\Cauchy {x_0} {\gamma} $\qquad$Cauchy Distribution $\CC$ $\quad:\quad$\CC $\qquad$that is: \mathcal C $\Cdm {f}$ $\quad:\quad$\Cdm {f} $\qquad$Codomain of Mapping $\ceiling {11.98}$ $\quad:\quad$\ceiling {11.98} $\qquad$Ceiling Function $30 \cels$ $\quad:\quad$30 \cels $\qquad$Degrees Celsius $\Char {R}$ $\quad:\quad$\Char {R} $\qquad$Characteristic of Ring, etc. $\Ci$ $\quad:\quad$\Ci $\qquad$Cosine Integral Function $\cis \theta$ $\quad:\quad$\cis \theta $\qquad$$\cos \theta + i \sin \theta $\cl S$ \quad:\quad\cl S \qquadClosure (Topology) $\closedint {a} {b}$ \quad:\quad\closedint {a} {b} \qquadClosed Interval $\cmod {z^2}$ \quad:\quad\cmod {z^2} \qquadComplex Modulus $\conjclass {x}$ \quad:\quad\conjclass {x} \qquadConjugacy Class $\cont {f}$ \quad:\quad\cont {f} \qquadContent of Polynomial $\ContinuousUniform {a} {v}$ \quad:\quad\ContinuousUniform {a} {v} \qquadContinuous Uniform Distribution $\cosec$ \quad:\quad\cosec \qquadCosecant (alternative form) $\Cosh$ \quad:\quad\Cosh \qquadHyperbolic Cosine $\Coth$ \quad:\quad\Coth \qquadHyperbolic Cotangent $\csch$ \quad:\quad\csch \qquadHyperbolic Cosecant $\Csch$ \quad:\quad\Csch \qquadHyperbolic Cosecant $\curl$ \quad:\quad\curl \qquadCurl Operator $\DD$ \quad:\quad\DD \qquadthat is: \mathcal D $\dfrac {\d x} {\d y}$ \quad:\quad\dfrac {\d x} {\d y} \qquadRoman \d for Derivatives $30 \degrees$ \quad:\quad30 \degrees \qquadDegrees of Arc $\Dic n$ \quad:\quad\Dic n \qquadDicyclic Group $\DiscreteUniform {n}$ \quad:\quad\DiscreteUniform {n} \qquadDiscrete Uniform Distribution $a \divides b$ \quad:\quada \divides b \qquadDivisibility $\Dom {f}$ \quad:\quad\Dom {f} \qquadDomain of Mapping $\dr {a}$ \quad:\quad\dr {a} \qquadDigital Root $\E$ \quad:\quad\E \qquadEuler's number $\EE$ \quad:\quad\EE \qquadthat is: \mathcal E $\Ei$ \quad:\quad\Ei \qquadExponential Integral Function $\empty$ \quad:\quad\empty \qquadEmpty Set $\eqclass {x} {\mathcal R}$ \quad:\quad\eqclass {x} {\mathcal R} \qquadEquivalence Class $\erf$ \quad:\quad\erf \qquadError Function $\erfc$ \quad:\quad\erfc \qquadComplementary Error Function $\expect {X}$ \quad:\quad\expect {X} \qquadExpectation $\Exponential {\beta}$ \quad:\quad\Exponential {\beta} \qquadExponential Distribution $\F$ \quad:\quad\F \qquadGalois Field $30 \fahr$ \quad:\quad30 \fahr \qquadDegrees Fahrenheit $\family {S_i}$ \quad:\quad\family {S_i} \qquadIndexed Family $\FF$ \quad:\quad\FF \qquadthat is: \mathcal F $\Fix {\pi}$ \quad:\quad\Fix {\pi} \qquadSet of Fixed Elements $\floor {11.98}$ \quad:\quad\floor {11.98} \qquadFloor Function $\fractpart {x}$ \quad:\quad\fractpart {x} \qquadFractional Part $\Frob {R}$ \quad:\quad\Frob {R} \qquadFrobenius Endomorphism $\Gal {S}$ \quad:\quad\Gal {S} \qquadGalois Group $\Gaussian {\mu} {\sigma^2}$ \quad:\quad\Gaussian {\mu} {\sigma^2} \qquadGaussian Distribution $\gen {S}$ \quad:\quad\gen {S} \qquadGenerator $\Geometric {p}$ \quad:\quad\Geometric {p} \qquadGeometric Distribution $\GG$ \quad:\quad\GG \qquadthat is: \mathcal G $\GL {n, \R}$ \quad:\quad\GL {n, \R} \qquadGeneral Linear Group $\grad {p}$ \quad:\quad\grad {p} \qquadGradient $\hav \theta$ \quad:\quad\hav \theta \qquadHaversine $\hcf$ \quad:\quad\hcf \qquadHighest Common Factor $\H$ \quad:\quad\H \qquadSet of Quaternions $\HH$ \quad:\quad\HH \qquadHilbert Space $\hointl {a} {b}$ \quad:\quad\hointl {a} {b} \qquadLeft Half-Open Interval $\hointr {a} {b}$ \quad:\quad\hointr {a} {b} \qquadRight Half-Open Interval $\ideal {a}$ \quad:\quad\ideal {a} \qquadIdeal of Ring $\II$ \quad:\quad\II \qquadthat is: \mathcal I $\map \Im z$ \quad:\quad\map \Im z \qquadImaginary Part $\Img {f}$ \quad:\quad\Img {f} \qquadImage of Mapping $\index {G} {H}$ \quad:\quad\index {G} {H} \qquadIndex of Subgroup $\inj$ \quad:\quad\inj \qquadCanonical Injection $\Inn {S}$ \quad:\quad\Inn {S} \qquadGroup of Inner Automorphisms $\innerprod {x} {y}$ \quad:\quad\innerprod {x} {y} \qquadInner Product $\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}$ \quad:\quad\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a} \qquadLimits of Integration $\invlaptrans {F}$ \quad:\quad\invlaptrans {F} \qquadInverse Laplace Transform $\JJ$ \quad:\quad\JJ \qquadthat is: \mathcal J $\KK$ \quad:\quad\KK \qquadthat is: \mathcal K $\laptrans {f}$ \quad:\quad\laptrans {f} \qquadLaplace Transform $\lcm \set {x, y, z}$ \quad:\quad\lcm \set {x, y, z} \qquadLowest Common Multiple $\leadstoandfrom$ \quad:\quad\leadstoandfrom $\len {AB}$ \quad:\quad\len {AB} \qquadLength Function: various $\LL$ \quad:\quad\LL \qquadthat is: \mathcal L $\Ln$ \quad:\quad\Ln \qquadPrincipal Branch of Complex Natural Logarithm $\Log$ \quad:\quad\Log \qquadPrincipal Branch of Complex Natural Logarithm $\map {f} {x}$ \quad:\quad\map {f} {x} \qquadMapping or Function $\MM$ \quad:\quad\MM \qquadthat is: \mathcal M $\Mult$ \quad:\quad\Mult \qquadMultiplication as a Primitive Recursive Function‎ $\NegativeBinomial {n} {p}$ \quad:\quad\NegativeBinomial {n} {p} \qquadNegative Binomial Distribution $\Nil {R}$ \quad:\quad\Nil {R} \qquadNilradical of Ring $\NN$ \quad:\quad\NN \qquadthat is: \mathcal N $\norm {z^2}$ \quad:\quad\norm {z^2} \qquadNorm $\O$ \quad:\quad\O \qquadEmpty Set $\OO$ \quad:\quad\OO \qquadthat is: \mathcal O $\On$ \quad:\quad\On \qquadOrdinal Class $\openint {a} {b}$ \quad:\quad\openint {a} {b} \qquadOpen Interval $\Orb S$ \quad:\quad\Orb S \qquadOrbit $\Ord {S}$ \quad:\quad\Ord {S} \qquad$$S$ is an Ordinal $\order {G}$ $\quad:\quad$\order {G} $\qquad$Order of Structure, and so on $\Out {G}$ $\quad:\quad$\Out {G} $\qquad$Group of Outer Automorphisms $\paren {a + b + c}$ $\quad:\quad$\paren {a + b + c} $\qquad$Parenthesis $\Poisson {\lambda}$ $\quad:\quad$\Poisson {\lambda} $\qquad$Poisson Distribution $\polar {r, \theta}$ $\quad:\quad$\polar {r, \theta} $\qquad$Polar Form of Complex Number $\powerset {S}$ $\quad:\quad$\powerset {S} $\qquad$Power Set $\PP$ $\quad:\quad$\PP $\qquad$that is: \mathcal P $\Preimg {f}$ $\quad:\quad$\Preimg {f} $\qquad$Preimage of Mapping $\pr_j \paren {F}$ $\quad:\quad$\pr_j \paren {F} $\qquad$Projection $\PV$ $\quad:\quad$\PV $\qquad$Cauchy Principal Value $\QQ$ $\quad:\quad$\QQ $\qquad$that is: \mathcal Q $\radians$ $\quad:\quad$\radians $\qquad$Radian $\displaystyle \int \map f x \rd x$ $\quad:\quad$\displaystyle \int \map f x \rd x $\qquad$Roman $\d$ for use in Integrals $\rD$ $\quad:\quad$\rD $\qquad$Differential Operator $y \rdelta x$ $\quad:\quad$y \rdelta x $\qquad$$\delta$ operator for use in sums $\map \Re z$ $\quad:\quad$\map \Re z $\qquad$Real Part $\relcomp {S} {A}$ $\quad:\quad$\relcomp {S} {A} $\qquad$Relative Complement $\rem$ $\quad:\quad$\rem $\qquad$Remainder $\Res {f} {z_0}$ $\quad:\quad$\Res {f} {z_0} $\qquad$Residue $\Rng {f}$ $\quad:\quad$\Rng {f} $\qquad$Range of Mapping $\RR$ $\quad:\quad$\RR $\qquad$that is: \mathcal R $\sech$ $\quad:\quad$\sech $\qquad$Hyperbolic Secant $\Sech$ $\quad:\quad$\Sech $\qquad$Hyperbolic Secant $\sequence {a_n}$ $\quad:\quad$\sequence {a_n} $\qquad$Sequence $\set {a, b, c}$ $\quad:\quad$\set {a, b, c} $\qquad$Conventional set notation $\ShiftedGeometric {p}$ $\quad:\quad$\ShiftedGeometric {p} $\qquad$Shifted Geometric Distribution $\Si$ $\quad:\quad$\Si $\qquad$Sine Integral Function $\Sinh$ $\quad:\quad$\Sinh $\qquad$Hyperbolic Sine $\size {x}$ $\quad:\quad$\size {x} $\qquad$Absolute Value, and so on $\SL {n, \R}$ $\quad:\quad$\SL {n, \R} $\qquad$Special Linear Group $\Spec {R}$ $\quad:\quad$\Spec {R} $\qquad$Spectrum of Ring $\sqbrk {a}$ $\quad:\quad$\sqbrk {a}  $\SS$ $\quad:\quad$\SS $\qquad$that is: \mathcal S $\Stab x$ $\quad:\quad$\Stab x $\qquad$Stabilizer $\struct {G, \circ}$ $\quad:\quad$\struct {G, \circ} $\qquad$Algebraic Structure $\StudentT {k}$ $\quad:\quad$\StudentT {k} $\qquad$Student's t-Distribution $\SU {n}$ $\quad:\quad$\SU {n} $\qquad$Unimodular Unitary Group $\Succ$ $\quad:\quad$\Succ $\qquad$Successor Function $\Syl {p} {N}$ $\quad:\quad$\Syl {p} {N} $\qquad$Sylow $p$-Subgroup $\Tanh$ $\quad:\quad$\Tanh $\qquad$Hyperbolic Tangent $\tr$ $\quad:\quad$\tr $\qquad$Trace $\TT$ $\quad:\quad$\TT $\qquad$that is: \mathcal T $\tuple {a, b, c}$ $\quad:\quad$\tuple {a, b, c} $\qquad$Ordered Tuple $\UU$ $\quad:\quad$\UU $\qquad$that is: \mathcal U $\var {X}$ $\quad:\quad$\var {X} $\qquad$Variance $\vers \theta$ $\quad:\quad$\vers \theta $\qquad$Versed Sine $\VV$ $\quad:\quad$\VV $\qquad$that is: \mathcal V $\WW$ $\quad:\quad$\WW $\qquad$that is: \mathcal W $\XX$ $\quad:\quad$\XX $\qquad$that is: \mathcal X $\YY$ $\quad:\quad$\YY $\qquad$that is: \mathcal Y $\ZZ$ $\quad:\quad$\ZZ $\qquad$that is: \mathcal Z

## Aligned Equations

To include aligned equations, a set of templates has been written: begin-eqn, eqn and end-eqn.

For more explanation, see Template:eqn.

## Specific Topics

### Commutative diagrams

See Help:Commutative Diagrams

## External references and manuals

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: