Runge's theorem

Runge's Theorem is a way to check if two equations mean the same thing. It's like a math balancing trick. Imagine you have two equations that each have different numbers like this:

1 + 3 = 4
2 + 2 = 4

You can use Runge's Theorem to check if these two equations are actually the same. You just add or subtract the same number to both equations. So for this example, we could add 2 to each equation like this:

3 + 3 = 6
4 + 2 = 6

Now the equations on both sides have the same sums, so that means that the two original equations (1 + 3 = 4 and 2 + 2 = 4) are the same! Runge's Theorem is a way to check if two equations are the same without having to solve them.