From: Stephen Turner (sret1_at_ntlworld.com)
Date: Fri Feb 01 2002 - 11:57:54 PST
176:5 VALID +2.0 Rich Holmes 2002-02-01 02:42:41 >>>>> A classic "proof" that 0 = 1 goes as follows: 1j = 1j property of equality 1j-1j = 0 subtract 1j from both sides (1-1)j = 0 distributivity of subtraction 0j = 0 1-1 = 0 j = 0/0 = 0j divide both sides by 0 1 = 0 QED divide both sides by j The fallacy is of course that fantasy subtraction (and addition) are not distributive. Future rule writers would do well to bear this in mind. <<<<< Judgement: Valid. The usual phrase is "multiplication is distributive over addition" but the meaning is obvious here, so that's not enough to make it invalid. Style: A very nice reply to 176:4, working out the consequences of the new maths introduced there. You're absolutely right, of course, distributivity must fail when we allow infinities in our system. However, although it's very clever I do doubt whether the restriction is in fact restrictive at all. It may lead to some subtle traps but I suspect that it won't in fact cause any trouble. -------------------------------------------------------------------------- -- Stephen Turner, Cambridge, UK http://homepage.ntlworld.com/adelie/stephen/ "This is Henman's 8th Wimbledon, and he's only lost 7 matches." BBC, 2/Jul/01 -- Rule Date: 2002-02-01 19:58:39 GMT
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