Exercise 16.
Your “friend” has shown you a “proof” he wrote to show that \(1 = 3\text{.}\) Here is the proof:
Proof.
I claim that \(1 = 3\text{.}\) Of course we can do anything to one side of an equation as long as we also do it to the other side. So subtract 2 from both sides. This gives \(-1 = 1\text{.}\) Now square both sides, to get \(1 = 1\text{.}\) And we all agree this is true.
What is going on here? Is your friend's argument valid? Is the argument a proof of the claim \(1=3\text{?}\) Carefully explain using what we know about logic.