[Moderator's note: Moved from another forum and slightly edited.] While teaching myself Calculus, I ran into a concept that is both simple and perplexing (to me, anyway). While I understand slope (m) as being X2-X1/Y2-Y1. Simple enough. But then there is talk of instantaneous slope. As if the difference between X1 and X2 or Y1 and Y2 are so small as to be nonexistent. I find this impossible. I have a similar issue with the tangent of a point as well, for basically the same reason. I am not looking for the mathematical explanation but rather the logical one. In a nutshell: How can a point have measurable slope or tangent? Sure would appreciate it if someone can explain this in 'everyday' terms. My mind, she is, how you say "boggled".