I like this, but I'll also contend that it's part of a broader question in applied math: What does it mean to be zero? One way to define this is to say that a

I like this, but I'll also contend that it's part of a broader question in applied math: What does it mean to be zero? One way to define this is to say that a vector is zero when it's orthogonal to every other vector in some space. This gives rise to Galerkin and Petrov-Galerkin methods to solve differential equations. However, it also gives rise to linear system solvers such as conjugate gradient (CG). Another way to define zero is to say that a vector is zero when it's norm is zero. This gives rise to least-squares finite element methods to solve differential equations. It also gives rise to linear system solvers such as GMRES. Anyway, I agree with you, but wanted to add that it's an idea part of a greater strategy that gives rise to a huge number of good algorithms.