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Q&A #267 |
From: Mr. Leohr
To: Teacher2Teacher Public Discussion
Date: 2003111900:50:18
Subject: Another fun proof that shows 2 = 1
Here's another proof that shows 2 = 1 that requires some knowledge of infinite series. If S = 1 - 1/2 + 1/3 - 1/4 + 1/5 ... and 2S = 2 - 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 ... which can be simplified by grouping terms to 2S = (2-1) - (1/2) + (2/3 - 1/3) - 1/4 ... 2S = 1 - 1/2 + 1/3 - 1/4 + 1/5 ... So 2S = S and if we divide both sides by S then 2 = 1 Here's where we went wrong... In infinite series, you are not allowed to reorder the elements. It is not commutative under addition. Crazy huh? Mr. Leohr
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