This question will probably be subjective and somewhat disliked because of this, but I can't get it out of my head. In mathematics something that is often taken for granted and even used as insults to other people is making it look like someone else claims something as ridiculous as "$2+2=5$".
Does there exist any algebraic (easy-to-understand) as well as useful construction which allows us to assign $2+2=5$?
Own work : The thing I have come up with so far is counting steps on an escalator. I take 2 steps two times and end up having traveled a total distance of 5 steps with respect to inertial frame (because escalator is moving). $4$ steps is due to my own motion and $1$ step would be the distance the escalator "boosted" me with. What would such an algebra look like? What would it be called? Would a simple group suffice?