If a function *almost* has some nice property, you can *quotient* out by
that property to make that nice property true.

For example, covariance is a symmetric bilinear form on the space of random variables with finite second moments. But it can be strengthened into an inner product by modding out by difference by a constant. (Two random variables are considered the same if they differ by a constant under this equivalence relation).

This makes covariance positive-definite instead of just positive
*semi*-definite. And now itâ€™s an inner product.