One counter example is sufficient to disprove any law of mathematics. However, if you ask how many examples that follow a hypotheses or a conjecture would prove it, the answer is that no matter how many examples you can show that follow a stated hypothesis, that is not a proof that the conjecture is true.

One of the most famous example of this is the Riemann Hypothesis which for approximately 150 years has defied the efforts of some of the best mathematicians, and remains unsolved. Without getting into the details of the problems suffice it to say that 10 trillion zeros performed as the conjecture predicts, however there is still a chance that the hypothesis is false. (see Ed Pegg Jr. “Ten Trillion Zeta Zeros”)

A proof is a proof, and example are examples!

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Tags: number theory, proof by example, Riemann Conjecture, Riemann Hypothesis, unsolved problems

This entry was posted on March 1, 2015 at 3:26 pm and is filed under General interest, Internet article or paper, Readings, Statistics Readings. You can follow any responses to this entry through the RSS 2.0 feed.
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