What is the meaning of dx?

Daily reminder that infinitesimals are heresy and [math]1-0.999...=0[/math].

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Fuck off, there is no meaning. It's not a mysterious infintesimal number or whatever, this is a lie "calculus" teachers tell to please the brainlets

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Depend on the context, if you are talking about the [math]dx[/math] in [math] \int f(x) dx[/math], it is simply there to tell you the variable you are integrating.
If you are calculating of the differential of a function [math] f [/math] , let say a function of 2 variable, then [math] df(x,y)=\frac{\partial f}{\partial x}(x,y) dx + \frac{\partial f}{\partial y} (x,y) dy[/math], then the dx and dy are map defined as : [math] dx(h,k)=h]/math] and [math]dy(h,k)=k[/math]
Is standard analysis, there is no such thing are infinitesimal change or whatever

A differential form. All the brainlets saying hurr durr infinitely small should kys themselves

it is a very small difference in x, so it is the same as delta x, but with the limit of xf -> xi
in the end, it does not have much numerical value, just algebrical and analytical, you can't calculate a value for it, trying to evaluating the limit gives you 0, and in many times it will be used as a variable

There's no red button on the real version of that meme, yours is wrong op.

Leibniz notation is cancer

it's a hugely small difference

I forgot about this meme

dx is a placeholder for the statement "with respect to delta x, as it gets closer to zero". there's no depth to this. it's like f(x) meaning "the function at the value x". it's all shorthand stuff because mathematicians are too weak willed to write long winded statements and concatenate everything.

in differential geometry (or just advanced calculus) it's a differential form
in basic calculus it's just notation and/or some handwaving bullshit

>engineering and science students in charge of pure mathematics

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Something about epsilon and delta or something I dunno lolol just ignore all the dumb proof bits.