My confusion here is it always seemed liked a simple mapping to take = to mean "make x equal to x+1" rather than "x is already equal to x+1". It is declaring a relationship, between the previous value and the current. One way or another, youre defining transformations. I mean even in the sum example, you see the statement "N is n-1" which is the exact same thing as x = x+1 with = swapped for "is"
That wasn't actually what the example said. It said N1 = N - 1, and continued using the N1 value somewhere else. In that example, no actual mutation occured.