Dx as change in distance vs dx as infinitesimal x?

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1. Feb 21, 2014

jaredvert

dx as change in distance vs dx as infinitesimal x???

Why are they the same notation?

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2. Feb 22, 2014

dipole

Because they're the same thing. What meaning exactly would $dx$ have otherwise?

If at time $t$ you have some position $x(t)$ then Newton's Law tells you how a small change in position is related to the velocity of the particle - namely $x + dx = x + v(t)dt$, where $v(t)$ satisfies the equation $m\frac{dv}{dt} = F$.

3. Feb 22, 2014

sophiecentaur

An actual change in distance is often denoted by δx or Δx, to distinguish it from the infinitesimal dx, which is part of Calculus. dy/dx really means the limit of δt/δx as δx approaches zero. In Science, we are often too sloppy about these notations as there may be pitfalls when you don't stick to the 'rules' precisely.