I think I understand it, let's see if I can explain it. Hopefully I'll say something useful. Take a vector for normal space, [x, y, z]. We say each component o

I think I understand it, let's see if I can explain it. Hopefully I'll say something useful. Take a vector for normal space, [x, y, z]. We say each component of this vector is one dimension, so this one is 3D, and each of its three components can vary. Two such vectors are different if one or more components differ between them. Treating a function as a vector means treating each distinct possible input to the function as a distinct component. For example, consider the integer function f(x) = x^2. This can be represented as the vector [..., 16, 9, 4, 0, 4, 9, 16, ...] Where the complete vector has as many components as integers. Since there's infinitely many integers, there's infinite components, so instead of 3D like the three component vector above, this vector is ∞D. Any single function is representable in this way, so each distinct function has its own unique infinitely long vector. So each different function is a different "point" in an infinite dimensional vector space.