**Question:** Can you provide an example of a claim where the base case holds but there is a *subtle* flaw in the inductive step that leads to a fake proof of a clearly erroneous result? [Note: Please do not answer with the very common all horses are the same color example.]

**Comment:** Sometimes inductive arguments can lead to controversial conclusions, such as the surprise exam paradox, Richard's paradox and a host of other paradoxes. However, I am interested in examples of a more mathematical nature (as opposed to linguistic) where the inductive argument is *subtly* flawed and leads to erroneous conclusions.

**Note:** If you provide an answer, please do so in a way similar to how current answers are displayed (gray out the flaw so people can be challenged to discover it).