I've been involved in a discussion on the definition of a tangent and would appreciate a bit of help.
At my high school and my college, I was taught that a definition of a tangent is 'a line that intersects given curve at two infinitesimally close points.' Aside from the possibility that tangent may elsewhere intersect the curve, to me, it was both intuitive and concise, but apparently, I'd have more chance of locating a set of hen's teeth than finding a similar definition online...
Has anybody else encountered such definition, or may have an objection to it (or an opinion on it, for that matter)? Thanks in advance.