Let V be an affine algebraic variety, and P be a point in V. V' is an irreducible component of V that contains P.
I want to prove the tangent space of P in V and the tangent space of P in V' have the same dimension, what i know is that dim$(T_{P}(V'))$ is smaller than dim$(T_{P}(V))$. But i don't know how to prove they are equal.
Thanks for your help!