^^What he's trying to refer to is the [wiki]idempotence[/wiki] property. However, he did it in a spectacularly stupid manner. Nobody ever uses A + A = A for the simple reason that the only value you can put to A in that case is 0. Sure, if you add 0 to 0, you'll end up with 0, but 0 is a cipher and useless for the analogy he was trying to make. So the standard way to write idempotence is A * A = A, which works if A = 1. What it really refers to is an operation that you can perform without changing the result.
But multiplication wouldn't have worked for his 'proof', so he needed to use addition, which meant he needed to cheat, and cheat stupidly, to make it work. As he himself put it, "If you use idempotency, it’s a reaction in mathematics where A + A = A. Actually in abstract algebra, A + A =2A but we are less concerned with the numerical value two. We are more less concerned with the symbols A, you find out that A + A will give you A showing that the whole thing goes unchanged."
Um, no, if A + A becomes 2A, then you did change it.
For an even better example of just how dumb he apparently is: "It didn’t change unlike commutativity A + B give B + A there is a change. A started the journey in commutativity and A + B gave us B + A and B started the journey after the equality sign."
Um, no, the commutative property simply means that you can change the order of the operations without changing the result. In other words, commutativity refers to a change that makes no difference.
I so want to smack this stupid moron of a grad student. Where is Astreja and her Clue-By-Four when you need it?