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## Homework Statement

Prove that any function [itex] f(x)[/itex] can be approximated to any accuracy by a linear combination of sign functions as:

[itex] f(x) ≈f(x_{0})+ \sum{[f(x_{i+1})-f(x_{i})]} \frac{1+ sgn(x -x_i)}{2}[/itex]

## Homework Equations

## The Attempt at a Solution

Looks like taylors theorem with a forward difference replaced with the derievative. It seems like the function only accepts sequential values approaching x from the left. That's about it. Anyone has any ideas?

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