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How would you go about proving the following "theorem" deductively? If you can count...

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dotta12345 | Student, College Sophomore | Honors

Posted March 18, 2012 at 6:04 AM via web

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How would you go about proving the following "theorem" deductively? If you can count your money, you don't have a billion dollars

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted March 19, 2012 at 4:10 AM (Answer #1)

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I would provide an indirect proof as follows:

Assume that you have a billion dollars and you can count your money.

For ease of computation, assume all of your money is in the form of $100 bills, the largest bill in common circulation.

Lets also assume that you can count 1 bill per second, and that you count 18hrs. per day, 7 days a week.

There are 64,800 seconds in an 18 hour period. There are 10,000,000 $100 bills in a billion dollars (assuming the American interpretation of a billion as 1,000,000,000 -- the British version has 12 zeros )

Then it takes `10,000,000 -: 64,800~~154` days to count your money. Depending on your definition of ability to count your money (is 154 days of counting 18 hours a day non-stop reasonable?), it seems reasonable to suggest that you are not able to count your money.

** If we use the British version of a billion, it would take over 432 years **

Since we have reached a "contradiction"; we assumed you could count your money, but this is unreasonable; then the assumption that you have a billion dollars must be false.

Therefore, if you can count your money then you don't have a billion dollars.

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