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)) (${f}^{(n)}\!\left(a\right)$).