This https://math.stackexchange.com/questions/21199/is-frac-textrmdy-textrmdx-not-a-ratio … post points out that the English were even a little behind the rest of Europe in mathematics because of their insistence on sticking with the less intuitive Newtonian notation! So crazy what notation can do.
Inverse Function Theorem is the reason we can get away with treating dy/dx as a fraction. imho it also settles the debate of which derivative notation is superior.pic.twitter.com/OixITvAaBf
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The things that pride can do.. lol
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Saw a paper that also allows for the use of dx,dy as infinitesimals. Sometimes us physicists play fast and lose with these things...nice to get some support from the math kids :)
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Check out Abraham Robinson's non- standard analysis
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This is the easy part of the theorem: https://en.wikipedia.org/wiki/Inverse_function_theorem?wprov=sfti1 …
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i never really looked at the deltas of two different variables as a fraction but more as a ratio or a relation between two concepts though that is what a fraction is.
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