On 18/06/2021 12:24, Ameya Nagarajan wrote: > Alaric, I'm going to need that maths explained.
My pleasure! Short version: An Abelian group is commutative. Long version: A "group" in maths is a thing consisting of a set of values (eg, the integers) and an operation that combines two of them and produces a third (eg, addition). Note that if we chose division as the operation, we wouldn't have a group - because 1 divided by 2 is a half, which isn't an integer, so that operation doesn't produce a valid value in the group. But a group of real numbers and division is fine, as the result of dividing two real numbers is another real number. These things are useful because we can prove that all groups with some property or other have a bunch of other properties; then when we find a situation that's a group with that initial property we can tell it has the other properties. Now, an operation that commutes is one in which the operation is symmetrical - it doesn't matter what order you combine the two inputs. A + B = B + A. So addition commutes, but division doesn't; 1 divided by 2 is a half, 2 divided by 1 is 2. Not the same result! Anyway, a group whose operation commutes is known as an Abelian group, named after the mathematician Niels Henrik Abel. Abelian groups have a bunch of useful properties, so if a mathematician finds a group is Abelian, then they can tell a whole bunch of other stuff about it without any more work. More info here: https://en.wikipedia.org/wiki/Abelian_group -- Alaric Snell-Pym (M0KTN neé M7KIT) http://www.snell-pym.org.uk/alaric/
