Induction is often incorrectly used by beginning students by ‘extending it to infinity’ . For example suppose the problem is the following: Problem: Prove/Disprove that the product of $\mathbb{N}$ number of countable sets is countable. Often many students show this kind of reasoning: since the product of two sets is countable, and the product of three sets is countable and if we know that the product of $n$ sets is countable then so is the product of $n+1$ sets, therefore we can conclude by induction that the product $\mathbb{N}$ number of countable sets is countable. The problem with this kind...