Why does 1 plus 1 gives you 2?

Answer 1

It follows directly from the definition of what 1, 2, and "plus" are. 1 and 2 are simply symbols that are associated with a particular quantity. For example, 1 ampersand is: &. 2 ampersands are: &&. 3 ampersands are &&&.

Addition can be defined by taking two sets, combining them into one set, and counting the number of things in the set. So If we take a set of ampersands that has 1 ampersand (&) and another that has 1 ampersand (&), combine those sets of ampersands into a single set (&&) and count the number of ampersands in it, then we have proved that 1 + 1 = 2.