For

For(x, ...) binds the symbol x as a local variable in its parent expression; the further arguments give a range, set or point whose meaning depends on the parent operator. For(x, S) iterates over a set, optionally followed by a filter predicate P(x), as in Set(f(x), For(x, S), P(x)) (\left\{ f(x) : x \in S\,\mathbin{\operatorname{and}}\, P(x) \right\}) or Sum(f(x), For(x, S)) (\sum_{x \in S} f(x)). For(x, a, b) lets x run between endpoints, as in Sum(f(n), For(n, a, b)) (\sum_{n=a}^{b} f(n)) or Integral(f(x), For(x, a, b)) (\int_{a}^{b} f(x) \, dx). For(x, a) lets x approach a point or selects a point of differentiation, as in Limit(f(x), For(x, a)) (\lim_{x \to a} f(x)) or Derivative(f(x), For(x, a)) (f'\!\left(a\right)), and For(x, a, n) gives the order of a derivative, as in Derivative(f(x), For(x, a, n)) ({f}^{(n)}\!\left(a\right)).