Quick question on Mathematical Induction

  • Mathematica
  • Thread starter Residual
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  • #1
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Main Question or Discussion Point

In mathematical Induction, sometimes two variables are given, such as:
"All positive integers n and all real numbers x >= -1."

My question is do you solve this normally and just keep x as itself or do you have to expand it like you do with n, making it k + 1 etc etc.

Thanks in advanced
 

Answers and Replies

  • #2
1,250
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You leave $x$ as it is, it is an arbitrary real number >= -1. In the proof it is like that you will need the fact x >= -1.
A little more context would help, but if I am guessing your issue correctly the answer is no.
 
  • #3
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Well an example would be:

|x^n| = |x|^n for every positive integer n and real number x.
 
  • #4
370
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You show for any given n, x works.

Which kind of makes sense, don't you think?
 
  • #5
3
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I have done a few examples and they all worked nicely.

Thanks.
 

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