In physics, this is why we call the derivative operator the "generator of translations"pic.twitter.com/iqJoydnylt
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You have it backwards! Translations give us enough to define derivatives...
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I do have yet to comprehensively justify myself, but I will say algebraic calculus one is almost finished, as in enroll-able by the larger public. The implication being that all basic calculus from 1-3 that's not the direct computation of a limit itself is finitely justified.
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I’m not sure of what you just said there
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