It's not simply notation, since you can prove the identity from base principles. An alien species would be able to discover this independently.
jsomae
you... you think you can choose not to be LGBTQ? I can only assume at this point you are trolling me.
This really fits my two hot takes about how we need to fix the left:
- (1) end purity tests: an imperfect ally is still an ally.
- (2) we need to appeal to centrists more; ± straight cis white men feel alienated when we talk about privilege as though it's a bad thing. We could talk about privilege as though it's a great thing that you should be proud of instead. Then we'd have privileged allies, which would be really helpful.
Why would you assume I don't have the context? I have a degree in math. I could be wrong about this, I'm open-minded. By all means, please explain how infinitesimals don't have a consistent algebra.
Not very good mathematicians if they tell you they aren't fractions.
e^𝘪θ^ is not just notation. You can graph the entire function e^x+𝘪θ^ across the whole complex domain and find that it matches up smoothly with both the version restricted to the real axis (e^x^) and the imaginary axis (e^𝘪θ^). The complete version is:
e^x+𝘪θ^ := e^x^(cos(θ) + 𝘪sin(θ))
Various proofs of this can be found on wikipeda. Since these proofs just use basic calculus, this means we didn't need to invent any new notation along the way.
try this on -- Yes 👎
It's a fraction of two infinitesimals. Infinitesimals aren't numbers, however, they have their own algebra and can be manipulated algebraically. It so happens that a fraction of two infinitesimals behaves as a derivative.
I guess Ty changed their name
oh huh, neat. Always though of those as "operations."
In Comp-Sci, operators mean stuff like >>
, *
, /
, +
and so on. But in math, an operator is a (possibly symbollic) function, such as a derivative or matrix.
it's legit a fraction, just the numerator and denominator aren't numbers.
toby fox