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I hope your answer for this question will help me understand a lot of things. Thank you guys.

Michael Hardy
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sourav suresh
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    This is a good question, easy to answer badly and harder to answer well. I hesitate to post anything$,\ldots\qquad$ – Michael Hardy Aug 20 '17 at 04:14
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    By definition of limit, $ \lim_{\Delta x\to 0} \Delta x=0$. –  Aug 20 '17 at 04:21
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    $dx$ is mainly a notation used for integration, derivation, differential forms,... Your question lacks some context: what is this lot of things that you hope to understand with this question's answers? – Gribouillis Aug 20 '17 at 04:31
  • Related: https://math.stackexchange.com/questions/143222/what-does-dx-mean (and many other questions on this site). – Hans Lundmark Aug 20 '17 at 08:09
  • I find the notations of calculus confusing a little. I'm 17 years old and I'm from India. Hard to find math enthusiasts and intellectuals here. dx/dy looks like division. The notation seems deceiving when we look at it in a basic algebraic point of view. Please correct me when I'm wrong and suggest changes. – sourav suresh Aug 21 '17 at 17:23
  • sexy question !! – rash Jun 16 '19 at 10:04

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Under conventional definitions $\lim\limits_{\Delta x\,\to\,0} \Delta x =0,$ whereas $dx,$ is not really defined in a logically rigorous way under currently conventional definitions, but it has a traditional (as opposed to either conventional or logically rigorous) definition. The quantity $dx$ was introduced int he 1600s by Leibniz and is supposed to represent an infinitely small change in $x$. If $y$ is a function of $x$ then $dy$ is the corresponding infinitely small change in $y$.

Even though $\lim\limits_{\Delta x\,\to\,0} \Delta x=0$ and consequently $\lim\limits_{\Delta y\,\to\,0} \Delta y =0,$ nonetheless $\lim\limits_{\Delta x\,\to\,0} \dfrac{\Delta y}{\Delta x}$ is some particular ordindary, usually nonzero, finite number.

Michael Hardy
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