Subtle and witty

Today, Professor Kiselev, my math professor from Russia, wrote a theorem on the board about Reimann sums and integrability. The theorem was an 0ˆ6if and only if0ˆ7 statement, meaning that if you assume a function is integrable, then you can prove it0ˆ9s Reimann sum converges to the integral, and conversely that if you assume the Reimann sum converges to the integral, the function is integrable. To prove an 0ˆ6if and only if0ˆ7 theorem, you must essentially do two proofs.

He asked the class to vote on which proof we thought would be easier. Out of twenty people in the class, three voted that it is easier to assume integrability, then prove the Reimann sums converge; four voted that the converse is easier.

This slight majority was in error: it is trivial to prove that if a function is integrable, its Reimann sum converges to the integral. Upon demonstrating this, Professor Kiselev said in his thick Russian accent,
0ˆ6Clearly, democracy does not always work.0ˆ7

It was priceless. Subtly and witty.
He0ˆ9s an amazing professor. My study group is going to nominate him for a Quantrell award.

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