Wikipedia:WikiProject Mathematics/Conventions

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This page is to collect up various mathematics conventions used in Wikipedia. Where there is not complete consensus in the mathematical literature, we want to make consistent choices across articles.

It should not be assumed that the readers of articles are familiar with the conventions listed here. Therefore, when an article could be misunderstood if interpreted according to a convention that is reasonably current in the mathematical literature, the article should make a note of that fact in situ.

[edit] Proposals for new conventions

If you wish to propose a convention that is not already reasonably standard here, add to the top of the list below, and start a discussion on the talk page. Leave the discussion open for at least two weeks, before implementing any large-scale edits based on the convention. Don't assume everyone concerned is watching this page.

(Notational) In coding theory articles, use "(n,k,d)-code" for regular (non-linear) codes non-linear code of length n, r codewords, and minimum distance d. Use "[n,k,d]-code" for linear codes of length n, rank k, and minimum distance d.
(Notational) In sequences or series, when listed with ellipses, include all terms up to the third term that has the changing coefficient, exponent, or index and the last term if the sequence or series is finite (e.g. '1, 2, 3, ..., 10'; in ' $a,\ ar,\ ar^2,\ ar^3,\ ar^4,\ \ldots$ ': use five terms because the first two terms do not contain the changing exponent). If the sequence or series has alternating signs, include all terms up to the fourth term that has the changing coefficient, exponent, or index (e.g. '1 - 2 + 3 - 4 + ...').

[edit] Terminology conventions

These should be regarded as mandatory; any article needing another convention should say so clearly

Compact spaces are not assumed Hausdorff (contra Bourbaki, who uses quasi-compact for our notion of compactness).
See completely Hausdorff space.
A ring is associative and unital (Exception: rings of operators, such as * algebras, B* algebras, C* algebras need not be unital).
A local ring is not assumed noetherian (contra Zariski).
In scheme theory, the older terminology of preschemes is not used (but scheme (mathematics) and separated scheme).
For Clifford algebras use v² = +Q(v).
The weight k of a modular form follows a currently-accepted (Serre) convention (so f(−1/τ) = τ^kf(τ) for level k), and q = e^2πiτ.
Elliptic functions are written in ω = half-period style.
Directed sets are preordered sets with finite joins, not partial orders as in, e.g., Kelley (General Topology; ISBN 0-387-90125-6).
An algebraic variety is assumed to be an irreducible algebraic set.
A lattice need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.

[edit] Notational conventions

These are advisory. Articles not adopting them may confuse the reader, and therefore should make an effort to be clear about the notation in use

The abstract cyclic group of order n, when written additively, has notation Z_n, or in contexts where there may be confusion with p-adic integers, Z/nZ; when written multiplicatively, e.g. as roots of unity, C_n is used (this does not affect the notation of isometry groups called C_n ).
The standard notation for the abstract dihedral group of order 2n is D_n in geometry and D_2n in finite group theory. There is no good way to reconcile these two conventions, so articles using them should make clear which they are using.
Bernoulli numbers are denoted by B_n, and are zero for n odd and greater than 1.
In category theory, write Hom-sets, or morphisms from A to B, as Hom(A,B) rather than Mor(A,B) (and with the implied convention that the category is not a small category unless that is said).
The semidirect product of groups K and Q should be written K ×_φ Q or Q ×_φ K where K is the normal subgroup and φ : Q → Aut(K) is the homomorphism defining the product. The semidirect product may also be written K ⋊ Q or Q ⋉ K (with the bar on the side of the non-normal subgroup) with or without the φ.
- The context should clearly state that this is a semidirect product and should state which group is normal.
- The bar notation is discouraged for reasons outlined on the talk page.
- If the bar notation is used it should be entered as {{unicode|⋉}} (⋉) or {{unicode|⋊}} (⋊) for maximum portability.
Subset is denoted by $\subseteq$ , proper subset by $\subsetneq$ . The symbol $\subset$ may be used if the meaning is clear from context, or if it is not important whether it is interpreted as subset or as proper subset (for example, $A\subset B$ might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that $A = B$ ). All other uses of the $\subset$ symbol should be explicitly explained in the text.
For a matrix transpose, use X^T (not X^T) or $X T$ (not $X T$ or $X^\top$ ).
In a lattice, infima are written as a∧b or as a product ab, suprema as a∨b or as a sum a+b. In a pure lattice theoretical context the first notation is used, usually without any precedence rules. In a pure engineering or "ideals in a ring" context the second notation is used and multiplication has higher precedence than addition. In any other context the confusion of readers of all backgrounds should be minimized. In an abstract bounded lattice, the smallest and greatest elements are denoted by 0 and 1.