Hi im pretty stuck on a proof so any help would be great:
Let P and Q be two projective curves, and let p belong to both of them. Show that the intersection number of P and Q at p is equal to one iff the tangent lines to p of P and Q are distinct
NB-we have defined intersection numbers in terms of the resultant, and i also do not take algebra this term so all of the results in terms of ideals and such on the internet are of no use to me
thanks
i should also probably say that we are working in P^2