Asked by Anonymous
How does mathematical induction work?
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Answered by
MathMate
It's a two step process that is used frequently in number theory. The first step is to prove that a hypothesis is valid for case 0, ad case 1.
The second step is to prove that <b>if</b> a general case <i>n</i> is true, <b>then</b> case <i>n+1</i> is also true.
This completes the proof, sinc8e if case 0 is true, then case 1 is true. If case 1 is true, then case 2 is true, and so on... ad infinitum.
For more information and history, see:
http://en.wikipedia.org/wiki/Mathematical_induction
The second step is to prove that <b>if</b> a general case <i>n</i> is true, <b>then</b> case <i>n+1</i> is also true.
This completes the proof, sinc8e if case 0 is true, then case 1 is true. If case 1 is true, then case 2 is true, and so on... ad infinitum.
For more information and history, see:
http://en.wikipedia.org/wiki/Mathematical_induction
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