Things to check

• Is the “statement function”  P  clearly and correctly defined? Is  P(n)  clearly and correctly stated?
  
  
• Is the base case stated and proved correctly? Is there a clear distinction between the statement of what one wants to prove (e.g.,  P(1))  and the proof of this? If the proof is not trivial, is it NOT backwards?
  
  
• When doing the inductive step, is the induction hypothesis (IH) -- e.g.,  P(n)  or  P(k)  -- clearly and correctly stated? Is it stated that IH is being assumed to be true? Is the possible range of values of  n  (or  k)  clearly stated?  (E.g., “for some  n > 0 ... ” )
  
  
• In the induction step, is  P(n+1)  (or  P(k+1))  stated correctly?
  
  
• In the induction step, is there a clear distinction between the statement of what one wants to prove (e.g.,  P(n+1))  and the proof of this? Is the proof correct? Is the proof NOT backwards? Is the point where the IH is used in the proof clearly indicated?
  
  
• Are the results summarized at the end of the proof?

See also Induction Guidelines and Format.

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Last modified Apr 11, 2008