2+2=?

Once upon a time, a profound question dawned on the mind of a king: "What is 2+2 ?". Having failed to answer it himself, he appointed three learned men: a physicist, an engineer, and a mathematician, to find the answer. He promised to provide all requisite resources (including government funding).

The physicist spent a day in his lab and, the following morning, declared: "2+2=3.9". The engineer spent days with his slide rule, and finally came to the king and concluded: "2+2=4.01 with an error bound of 10-2". However, there was no sign of the mathematician.

A few months later, the mathematician came running into the king's court, joyous, and in much the same attire as when Archimedes had said "Eureka!". The king asked him "Did you find the value of 2+2?" The mathematician replied "I have not found the value yet, but I have proved that the sum exists."

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