(New page: The Principle of Induction: Goal: Collection of statements <math>P_0,P_1...P_i</math> that we want to prove. Idea: Prove <math>P_0</math> explicitly. Design a crank/el...) |
|||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The Principle of Induction | + | [[Category:MA375]] |
| − | + | [[Category:math]] | |
| + | [[Category:discrete math]] | ||
| + | |||
| + | =[[MA375]]: The Principle of Induction= | ||
| + | ---- | ||
| + | Goal: Collection of statements <math>P_0,P_1...P_i</math> that we want to prove. | ||
Idea: Prove <math>P_0</math> explicitly. | Idea: Prove <math>P_0</math> explicitly. | ||
Design a crank/elevator that proves the following | Design a crank/elevator that proves the following | ||
| − | + | Since <math>P_0</math> has been proven to be true, it shows that there is at least one<math>P_i</math> which is 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. | ||
| + | |||
| + | |||
| + | *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) | ||
| + | ---- | ||
| + | [[Main_Page_MA375Fall2008walther|Back to MA375 Fall 2008]] | ||
Latest revision as of 05:41, 21 March 2013
MA375: 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)
