Math Induction: Where Does the >2xk Come From?

[coconut62]

Please refer to the image attached.

Where does the > 2 x k come from?

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

 

[rbj]

look two lines above the questioned statement.

 

[coconut62]

I got it, thanks.

 

[coconut62]

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?

 

[Mark44]

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.

 

[Amir Livne]

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 2^{k+1} > k + k \ge k+1 and together 2^{k+1} > k+1.