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## Main Question or Discussion Point

I just want to know why in the world this works?

I am speaking about the simple iteration of taking a function,

For example the function :

Setting it to 0 and solving for x:

and then you pick a 'guess' and iterate.

Why in the world does the iteration narrow down onto the root? It seems so arbitrary. We just keep plugging in the values, keep iterating on, and it just converges on the root.

Why oh why is this behavior so? Btw, I promise to learn LaTeX soon..so it won't look as funky next time.

I am speaking about the simple iteration of taking a function,

**f(x)**, setting it to 0,**f(x) = 0**, solving for x in the function and setting it equal to g(x)...and then iterating.For example the function :

**f(x) = x^2 +2x - 1**Setting it to 0 and solving for x:

**x = (1 - 2x)/x**and then you pick a 'guess' and iterate.

Why in the world does the iteration narrow down onto the root? It seems so arbitrary. We just keep plugging in the values, keep iterating on, and it just converges on the root.

Why oh why is this behavior so? Btw, I promise to learn LaTeX soon..so it won't look as funky next time.