Proof by mathematical induction

Thread Starter

asilvester635

Joined Jan 26, 2017
73
Before we start, my textbook declares lgn as base two.

I only have one question, how did log2 become n (both highlighted in yellow in the picture)? Is it because log2 = 1, which is too small to even matter? Below is a link of the equations.

20170207_091636000_iOS.jpg
 

wayneh

Joined Sep 9, 2010
17,153
Is it because log2 = 1, which is too small to even matter?
Glad you got it. I just wanted to point out that mathematicians don't think that way. An engineer might put a slash through a term that is numerically insignificant to the overall equation, but a mathematician would never do that.
 

WBahn

Joined Mar 31, 2012
26,398
Wanted to emphasize what wayneh said. Mathematical proofs have no room for approximations of any kind. A proof is a statement of irrefutable fact (provided it contains no errors) that is exact and precise. It may have qualifications, such as saying that n has to be greater than 2 because the claim doesn't hold when n is equal to 2, but that's fine.
 
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