Tangent vectors are, in this formalism, given in terms of a basis of differential operators of the first order, ∂ ∂ ∂ ∂ x μ μ | p , where p is an event. This operator applied to a function f gives the directional derivative of f at p in the direction of increasing x with x, ν ≠ μ fixed. They provide a basis for the tangent space at p.