> A unit is an operation you can apply multiple times and get back to the starting point, for example multiplication by 1 or -1. Nope. That is an idempotent[1]

> A unit is an operation you can apply multiple times and get back to the starting point, for example multiplication by 1 or -1. Nope. That is an idempotent[1], or a root of unity, i.e. x^n = 1 for some n >= 0. A unit is something which has an inverse, though that inverse need not be a power of x itself. For example, 1/2 is inverse to 2 in the rational numbers. [1]: https://en.wikipedia.org/wiki/Idempotence https://en.wikipedia.org/wiki/Idempotence