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Quick question on Mathematical Induction

  1. Mar 12, 2007 #1
    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
  2. jcsd
  3. Mar 12, 2007 #2
    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.
  4. Mar 12, 2007 #3
    Well an example would be:

    |x^n| = |x|^n for every positive integer n and real number x.
  5. Mar 12, 2007 #4
    You show for any given n, x works.

    Which kind of makes sense, don't you think?
  6. Mar 12, 2007 #5
    I have done a few examples and they all worked nicely.

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