Inverting an operation is often difficult because the inverse is not unique. For example, a positive number has two square roots, one positive and one negative (22 = (–2)2 = 4). Most famously, integrating the derivative of a function only recovers the function up to a constant. The derivative of a function tells us how much that function goes up or down at each point. Adding up all those changes gives us the function back, except we don’t know where it started; we can “slide” the integrated function up or down without changing the derivative.
