Could a function be found for any set of points, assuming those points didn't contradict the definition of function?
I mean, given a bunch of (x, y) pairs, could a function be found where when you input the x given in each pair, the output is the y?
I've run into many questions like this in highschool mathematics. Questions like "Find a function who's graph goes through the points (-5,10) and (7,-10)". Now I'm wondering if a function could be found no matter which points, and no matter how many points you're given.
Also, is there any method for finding these functions? Any applications of this? Any more information on the idea? I'm just looking for information about this thing I've been wondering about.