Induction Proof: Consider the following induction "proof" that all sheep in a flock are the same color:

Base Case: One sheep. It is clearly the same color as itself.

Induction step: A flock of n sheep. Take a sheep, a, out of the flock. The remaining n - 1 are all the same color by induction. Now put sheep a back in the flock, and take out a different sheep, b. By induction, the n - 1 sheep (now with a in their group) are all the same color. Therefore, a is the same color as all the other sheep; hence, all the sheep in the flock are the same color.

What is wrong with this "proof"?

3. Induction Proof Consider the following induction proof that all sheep in a flock are the same color: Base case: One sheep. It is clearly the same color as itself. Induction step: A flock of n sheep. Take a sheep, a, out of the flock. The remaining n - 1 are all the same color by induction. Now put sheep a back in the flock, and take out a different sheep, b. By induction, the n - 1 sheep (now with a in their group) are all the same color. Therefore, a is the same color as all the other sheep; hence, all the sheep in the flock are the same color. What is wrong with this proof? 3. Induction Proof Consider the following induction proof that all sheep in a flock are the same color: Base case: One sheep. It is clearly the same color as itself. Induction step: A flock of n sheep. Take a sheep, a, out of the flock. The remaining n - 1 are all the same color by induction. Now put sheep a back in the flock, and take out a different sheep, b. By induction, the n - 1 sheep (now with a in their group) are all the same color. Therefore, a is the same color as all the other sheep; hence, all the sheep in the flock are the same color. What is wrong with this proof