Who told you about \(\frac{dy}{dx}\) but hided the information about \(\frac{f(x+dx)- f(x)}{dx}\) ?
Was it me or was it all the math books? And why should they, the mathematicians, have done so?
Why can't "usual mathematics" deal with something that is infinitely small?
What is the question? Is the question "is 1/∞ either 0 or non-zero?" ? The question does not have an unambiguous answer either 0 or non-zero, because 1/∞ is both.
If that is a stupid thing to do, then why don't you answer the question: "is 1/∞ either 0 or non-zero?" ?
Yes. But I am not talking about sets, because maybe it is not necessary right now. I am talking about finite difference f(x+h) - f(x) where h is finite, as opposed to f(x + dx) - f(x) where dx is not finite. Adjective finite refers to distance in this case, finite distance.
You can count the elements of X only if you know n. But because you did not tell what is n, I can't tell how many elements are there in X. So it may look as though dx
is a set for which you don't tell what is n.