Introducing definite integrals, which represent the net area under a curve. Learn what this exactly means and about the notation we use to write them.
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Yoni Smadja dx is the difference between two points . A difference which is almost equal to zero , but not zero . U might say this difference is equal to 1/100 or 1/1000 or 1/100000000 or 1/10000000000 , yes the amount of difference which I mentioned above is very very small and almost equal to zero , but they are still some values which you can see and count. dx is some thing that small that a human can't imagine . It's just a previous point before zero , which is obviously not understandable for humans.you can make any number as small as you can by putting more zeros in ur denominator as I did in above examples, but u can never achieve to a point which is just a previous point before zero.
So the conclusion of my comment is that dx which is a difference between two points
Let's say difference between points
X and a
so , dx = x - a
Such that x is almost equal to a
Which we say in mathematics as" x proceeds to a" . An arrow symbol is used to say this phrase which I don't have here.
Than you can say that
dx proceeds to zero
It's a very beautiful concept in mathematics derived by humans. As we are staying at a same point because x and a are almost equal but at the same time we find a difference at that point.
Hope.u get something..
PS: After you're done with Differential Calculus, It would be really great if you do the same approach of explaining the theory behind Linear/Multi-linear/Matricial and/or Tensor Algebra. Or maybe get into Stochastic Calculus as it's on the same lines of the current series. Applying your approach to these subjects would be really enlightening since they almost look daunting when you try to get to the bottom of the theory.
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