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Comment on UwU brat mathematician behavior

Phoenix3875@lemmy.world ⁨3⁩ ⁨months⁩ ago

I think rather d/dx is the operator. You apply it to an expression to bind free occurrences of x in that expression. For example, dx²/dx is best understood as d/dx (x²). The notation would be clear if you implement calculus in a program.

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bhamlin@lemmy.world ⁨3⁩ ⁨months⁩ ago
If not fraction, why fraction shaped?

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- Amir@lemmy.ml ⁨3⁩ ⁨months⁩ ago
  If you use exterior calculus notation, with d = exterior derivative, everything makes so much more sense
  
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yetAnotherUser@discuss.tchncs.de ⁨3⁩ ⁨months⁩ ago
I just think of the definition of a derivative.

d is just an infinitesimally small delta. So dy/dx is literally just lim (∆ -> 0) ∆y/∆x. which is the same as lim (x_1 -> x_0) [f(x_0) - f(x_1)] / [x_0 - x_1].

Note: ∆ -> 0 isn’t standard notation. But writing ∆x -> 0 requires another step of thinking: y = f(x) therefore ∆y = ∆f(x) = f(x + ∆x) - f(x) so you only need ∆x approaching zero. But I prefer thinking d = lim (∆ -> 0) ∆.

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