I am having a difficult time proving that the set of all polynomials of degree less than n with coefficients in a field K where K is the real numbers is isomorphic with the set of all functions with values in K defined on a set S where S consists of n distinct points of R.
This a problem in Peter Lax's Linear Algebra book which I am reading.
The concepts I am finding difficult about this problem is how to tell if these linear spaces are onto and one-to-one with each other. So if you can explain that a bit in-depth and step by step that would be great.
Thanks in advance for any help!