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Proof: more evens than odds

Permalink 09/17/10 at 03:21:20 am, by Ed, 163 words   English (US)
Categories: General

Alright, so I've devised a terrible proof that shows there are more even numbers than odd numbers. See how many things you can find wrong with it.

Assume the opposite: there are the same number of evens (e) and odds (o). Any pair of numbers can be one of three forms: both even, both odd, or one of each.

Now, it is common knowledge that two evens muliplied result in an even number. The converse is true with odds. That is two odds multiplied results in an odd. That covers two thirds of all possible results. The only remaining third is one even and one odd, which also results in an even number.

Based on our earlier assumption, that there are the same number of evens and odds, we can deduce that each of the three results can be weighted evenly. Ergo, there are twice as many even numbers as there are odd numbers. A contradiction!

Therefore, our original assumption must be false.

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