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| − | '''Proof of the Trashcan Theorem'''
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| − | The Theorem of Mathematical Correctness (TMC) states that people who are better at math are more likely to be correct in a math problem than a person who is not as good at math.
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| − | The math problem we are currently faced with is this:
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| − | Determine which of the following is greater:
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| − | 1) trashcan
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| − | 2) banana
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| − | mikechen argues that trashcan is greater, while Iamteehee thinks banana is greater. Since this is a math problem, we can use the TMC to determine who is more likely to be correct.
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| − | The only practical way to measure how good a person is at math is contest results. When both people are exceptionally good at math, results on standardized tests are completely useless. FTW rating has been proven to be too unreliable, and Alcumus can easily be cheated on. We see that mikechen got first in the State Mathcounts competitions this year, while Iamteehee got 6th. Also, mikechen's USAJMO index is 231, while Iamteehee's is 0. So, we know that mikechen is generally better at math than Iamteehee, which means that by TMC, mikechen is more likely to be correct in this problem than Iamteehee. Thus, the probability that trashcan > banana is more than 50%, so trashcan is expected to be greater than banana. If an object A is expected to be greater than an object B, then object A must be generally better than object B. Thus, trashcan is generally better than banana. Since we only need something to be "generally better" than another for it to be greater, we can now reach our final conclusion:
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| − | '''Thus, we have trashcan > banana, as desired.'''
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| − | This is the trashcan theorem. Q. E. D.
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