Mathematical induction

  • Thread starter coconut62
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  • #1
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Please refer to the image attached.

Where does the > 2 x k come from?

Based on the proposition, shouldn't it be > k+1?
 

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  • #2
rbj
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look two lines above the questioned statement.
 
  • #3
161
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I got it, thanks.
 
  • #4
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But one more thing: 2^(k+1) is equal or bigger than k+1. Then it's not necessarily bigger than k+1. How can we say that the proposition is true for that case?
 
  • #5
35,287
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But one more thing: 2^(k+1) is equal or bigger than k+1. Then it's not necessarily bigger than k+1. How can we say that the proposition is true for that case?
If k > 1, then 2k > k + 1.

2k = k + 1 only if k = 1.
 
  • #6
38
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Greater and Greater-Equal

But one more thing: 2^(k+1) is equal or bigger than k+1. Then it's not necessarily bigger than k+1. How can we say that the proposition is true for that case?


The propisition is true since it says [itex]2^{k+1} > k + k \ge k+1[/itex] and together [itex]2^{k+1} > k+1[/itex].
 

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