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There is some precedent for the notation (a, b) or <a, b> or [a, b] meaning "some function applied to a and b". For example, inner products or commutators (for
by wging 13y ago
There is some precedent for the notation (a, b) or <a, b> or [a, b] meaning "some function applied to a and b". For example, inner products or commutators (for a group, the commutator [a, b] of a and b is equal to a^-1 b^-1 ab).
The compactness really can matter sometimes... you might have a gcd appearing in the initializer of a summation symbol. http://en.wikipedia.org/wiki/Mobius_inversion http://en.wikipedia.org/wiki/Mobius_inversion gives you a good example of the "d divides n" notation appearing in such a position... pretty sure there exist similar constructions but with gcds.
- vog 13y agoAlso, when stretching analogies far enough, one could argue that the GCD serves a similar purpose in number theory like the inner product in linear algebra. :-) However, I think the real reason is the notation of GCD as an Ideal generated over two elements of a Ring, as described in the other reply: https://news.ycombinator.com/item?id=6090688 https://news.ycombinator.com/item?id=6090688