Proof
Let . For every input, we have . Therefore, . Using Fubini's theorem, since all terms are non-negative we can switch the order of summation, giving . By the Pigeonhole principle, there must exist an algorithm so that, concluding the proof.
As mentioned above, this theorem can also be seen as a very special case of the Minimax theorem.
Read more about this topic: Yao's Principle
Famous quotes containing the word proof:
“To cease to admire is a proof of deterioration.”
—Charles Horton Cooley (1864–1929)
“War is a beastly business, it is true, but one proof we are human is our ability to learn, even from it, how better to exist.”
—M.F.K. Fisher (1908–1992)
“It comes to pass oft that a terrible oath, with a swaggering accent sharply twanged off, gives manhood more approbation than ever proof itself would have earned him.”
—William Shakespeare (1564–1616)