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We have to show that <math>P_{i+1}</math> is also true. | We have to show that <math>P_{i+1}</math> is also true. | ||
Then, induction guarantees that every <math>P_i</math> is true. | Then, induction guarantees that every <math>P_i</math> is true. | ||
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| + | I thought it was interesting that today Uli pointed out there was no Nobel Prize for Math. It was also funny that he stated this is because Nobel's wife cheated on him with a math teacher.--[[User:Jahlborn|Jahlborn]] 22:41, 4 December 2008 (UTC) | ||
Revision as of 18:41, 4 December 2008
The Principle of Induction:
Goal: Collection of statements $ P_0,P_1...P_i $ that we want to prove. Idea: Prove $ P_0 $ explicitly. Design a crank/elevator that proves the following Since $ P_0 $ has been proven to be true, it shows that there is at least one$ P_i $ which is true. We have to show that $ P_{i+1} $ is also true. Then, induction guarantees that every $ P_i $ is true.
I thought it was interesting that today Uli pointed out there was no Nobel Prize for Math. It was also funny that he stated this is because Nobel's wife cheated on him with a math teacher.--Jahlborn 22:41, 4 December 2008 (UTC)
