The procedure of proving the validity of a proposition  Pn  for all integers  n ≥ k  includes the following three stages.

1.  Formulation of the of the induction basis.
    Example: There exists an integer  k  such that the statement  Pk  is true.
   
   
2.  Formulation of the induction hypothesis.
    Example: The statement  Pn  holds true for some integer  n ≥ k.
   
   
3. The induction step.
   Example: If the statement  Pn  implies  Pn+1 (provided that  n ≥ k) then  Pn  is true for all integers  n ≥ k.

However, if the statement  Pn  is false and  Pn  implies  Pn+1, then one can conclude that  Pn  is false for all integers  n ≤ k  but we can say nothing about the validity of  Pn  for  n > k.

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