## Suggestions for good notation

I occasionally come across a new piece of notation so good that it makes life easier by giving a better way to look at something. Some examples:

• Iverson introduced the notation [X] to mean 1 if X is true and 0 otherwise; so for example Σ1≤n<x [n prime] is the number of primes less than x, and the unmemorable and confusing Kronecker delta function δn becomes [n=0]. (A similar convention is used in the C programming language.)

• The function taking x to x sin(x) can be denoted by x ↦ x sin(x). This has the same meaning as the lambda calculus notation λx.x sin(x) but seems easier to understand and use, and is less confusing than the usual convention of just writing x sin(x), which is ambiguous: it could also stand for a number.

• I find calculations with Homs and ⊗ easier to follow if I write Hom(A,B) as A→B. Similarly writing AB for the set of functions from B to A is really confusing, and I find it much easier to write this set as B→A.

• Conway's notation for orbifolds almost trivializes the classification of wallpaper groups.

Has anyone come across any more similar examples of good notation that should be better known? (Excluding standard well known examples such as commutative diagrams, Hindu-Arabic numerals, etc.)

-
this question is broadly useful, so perhaps better as community wiki? – S. Sra Oct 20 2010 at 20:09
In set theory we write ${}^B A$ for the set of functions from $B$ to $A$. – Andres Caicedo Oct 20 2010 at 20:54
I've always assumed that the notation $A^B$ is because of the "exponential law" $(A^B)^C = A^{B\times C}$ ... – Kevin Lin Oct 20 2010 at 23:18
Arabic numerals ? Ah yes, they were transmitted to Europe by the Arabs. – Chandan Singh Dalawat Oct 21 2010 at 3:29
Isn't $x \mapsto f(x)$ commonplace? As for homomorphisms, they are not simply maps, and $\mathrm{Hom}(A, B)$ denotes the whole class, while $A \to B$ denotes a single mapping. – Kallikanzarid Oct 21 2010 at 3:38