Comment by graypegg

Just to toss on some info you might already know, the mention about grouping is related to group theory. [0] If a set satisfies those 3 axioms, there's some assertions you can build off that are common to all group theory sets, and having an identity element is one of them. It's weird that it's NOT zero, but in this case, infinity behaves LIKE zero. (Imagine going infinitely along the curve on the x-axis towards the open part of the curve, so therefore going infinitely up/down the y-axis. At somepoint, you're essentially have a vertical line between the original point, and your infinitely far away point, which points at the exact opposite side of the curve, which reflects back to the original point.) For natural numbers, zero is the identity, since X + 0 = X, in the same way P + infintelyfarawaypoint = P in this set.

To use a dumb analogy, it's polymorphism where your interface is something like regular old natural numbers: as long as your class behaves like natural numbers in some key ways, you can pass them to any add()/subtract()/multiply() functions relying on that behaviour.

[0] https://en.wikipedia.org/wiki/Group_(mathematics)#Definition