> [UPDATE] Let me put this more succinctly: how is it possible that there can be a continuous computable function whose derivative is uncomputable? What exactly is it about this function that makes numerical differentiation fail?
Like this
f(0) = 1
f(x!=0) = 0
It's more of a mathematical trick than anything else, it's not a "natural function" let's put it this way
Equality over computable reals is not decidable, so I don't think you've actually defined a computable function here. The issue is much more subtle than that.
Like this
f(0) = 1
f(x!=0) = 0
It's more of a mathematical trick than anything else, it's not a "natural function" let's put it this way