This is, I think, a fairly simple question, but I haven't been able to find an answer to. Is there any graph for which there's no way to describe it in terms of a polynomial, function, or any other formula? If so, why?
Asked
Active
Viewed 440 times
1
-
You can always define a function $f$ of two variables, such that $f(x,y)=1$ if the point $(x,y)$ is on the graph, and $f(x,y)=0$ otherwise. – mr_e_man Jan 22 '18 at 02:11
1 Answers
2
I can draw (any) arbitrary curve that represents a function, but measuring what that function is exactly (with infinite precision) from the drawing is an insurmountable task.
gt6989b
- 54,422
-
Can we simply use b-splines or Fourier series with infinite terms to describe potentially any drawings? – GENIVI-LEARNER Oct 28 '20 at 23:06
-
1@GENIVI-LEARNER the problem of keeping track of infinite number of coefficients exceeds the space available for computation – gt6989b Oct 29 '20 at 04:18
-