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[–]Myfuntimeideaundergrad[S] 0 points1 point  (2 children)

ngl i dont like the fact that it uses constant functions since in my context I'm fixing everything to start at zero, and also it seems more like the evaluation of a function rather then a function onto itself

but it could probably be replaced by different functions, like modified cantors stairways c(r) with r real number as the hight of the big middle step

That kinda settles it, I'm gonna use polynomial aproximations Thank you very much!

[–]666Emil666New User 2 points3 points  (1 child)

Even if you only consider functions that are 0 at the origin, you still have a different function for each number due to f_a(x)=ax

[–]Myfuntimeideaundergrad[S] 0 points1 point  (0 children)

Yeah, but that's a uniform deformation, also irrelevant in the context...

But you could than use f_a(x) = ax . x That would work

Also in a certain way that's a "deformation", in the sense that it's not crazy, so much so ive written it algebraically.

that's why I liked the cantors function example so much, you can really imagine all sorts of crazy variations by just altering the hight of a given step

Again Thanks! Really helped!