Possible Proof That 1 + 1 Does Not Equal 2Date: 04/19/2001 at 01:57:44 From: Desmond Leung Subject: A possible proof for 1+1 not equal 2 A buddy of mine told me how to prove that 1 + 1 does not equal 2, and some say he was correct. I just want verification. It goes something like this: 1 = 1/3 + 1/3 + 1/3 1 = 0.333... + 0.333... + 0.333... (... means repeated) 1 = 0.999... normally lim (1)^n = 1 n->inf but lim (0.999...)^n = 0 n->inf therefore lim [(0.999...)^n + (0.999...)^n] = 0 n->inf which does not equal 2. Would this work? Date: 04/19/2001 at 14:27:47 From: Doctor TWE Subject: Re: A possible proof for 1+1 not equal 2 Hi and thanks for writing to Dr. Math. Here's the problem with this "proof." lim (0.999...9)^n = 0 n->oo is true only if there is a *finite* number of 9's in the value in parentheses. With an infinite number of 9's, the expression becomes: oo lim [sum(9/10^k)]^n n->oo k=1 and we cannot conclude that this expression goes to zero. For more information on false "proofs" of this sort, see the Dr. Math FAQ at: http://mathforum.org/dr.math/faq/faq.false.proof.html I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ |
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