Love it!
Cordially, Ameya Nagarajan <http://www.linkedin.com/in/ameyann> On Fri, 18 Jun 2021 at 17:32, Alaric Snell-Pym <[email protected]> wrote: > 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/ > >
