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/sci/ - Science & Math

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6124511 No.6124511 [Reply] [Original]

Is this reasoning correct? So if a function is homomorphic and has a defined limit. If lim a->0 f(a)/a exists then f is differentiable everywhere, something seems wrong here but i dont know what, can anyone explain what im doing wrong?

>> No.6124536

literally all i see you doing is substituting values for a simple variable.

fuck if i know.

>> No.6124539

>>6124511
Sure, it's right. For example, suppose f(x)=m x +b. Then f'(x)=m=lim f(a)/a. Derivative is constant.

>> No.6124540

>>6124539
oops, you need b=0, but it works then.

>> No.6125263 [DELETED] 

holy crap no, that doesn't work. You can't go from f(x)-f(x0) to f(x-x0), I don't know where you're getting that from. And what does it have to do with homomorphism? Do you mean a holomorphic function?

>> No.6125277

you'll find that there aren't many continuous homomorphisms of (R,+).

>> No.6126330

>>6125277
Yes. Note that if f is differentiable at 0, then OP's paper is a proof that f is differentiable everywhere, with f'(x)=f'(0) for all x, so f(x)=f'(0)*x.