how to point out errors in proof by induction I have searched for an answer to my question but no one seems to be talking about this particular matter..
I will use the all horses are the same color paradox as an example.
Everyone points out that the statement is false for n=2 and that if we want to prove the propositions we should use 2 as the base case for this proof.
But, (as I see it..), you have to use reason to figure that out. 
My question is, is there anything wrong with induction itself? 
except for the fact that we can use reason to understand why the proof is faulty.
This goes for all these problematic propositions..
Thank you all!

The formulation that one horse cannot have different colors is mathematically correct,
 but useless for the case $n=2$. 
Since we need two horses to compare the colors, we
 cannot follow that two horses have the same color out of the trivial fact that one horse cannot have different colors. 
So, the induction step does not
 work from $n=1$ to $n=2$. Thus, the induction is false.
