In math, idempotence describes only unary functions that you can call on their own output. Math-idempotence is, “If you take the absolute value of a number, and then you take the absolute value of that, the result doesn’t change on the second (or subsequent) operations.” Math.abs is math-idempotent. Math-idempotence only applies to functions of one parameter where the parameter type and return type are the same. Not so useful in programming.

Programming-idempotence is about side effects. It’s about stuff that happens to the outside world when you call a function. Idempotence says “If you’ve called me once, it doesn’t matter whether you called me again.”