Algebra · Iteration
Chapter 1 · 3
The idea
Rearranging an equation into iterative form
How "show that the equation can be written as x = g(x)" works — isolate a lone x by honest rearranging — and why that form is exactly what an iteration machine needs.
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Algebra · Iteration
Rearranging an equation into iterative form
How "show that the equation can be written as x = g(x)" works — isolate a lone x by honest rearranging — and why that form is exactly what an iteration machine needs.
Why it works
Feeding a machine that eats x
The change-of-sign lesson trapped a root of between and — but trapping is not finding. The finder is an iteration machine: feed in a guess, and a better guess comes out. The catch is the machine's inlet shape. It only accepts equations written as— " equals a formula involving " — because that is what lets an estimate be fed in on the right to produce a new estimate on the left. So exam questions say: *"show that the equation can be rearranged to give ."* That step is the adapter, and it is pure rearranging.
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The rest of the explanation, plus 2 worked examples you step through move by move.
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