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Topic: Keith Devlin's Online Course
Replies: 88   Last Post: Jan 5, 2014 9:31 PM

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 Joe Niederberger Posts: 4,629 Registered: 10/12/08
Re: Keith Devlin's Online Course
Posted: Dec 30, 2013 2:41 PM

R Hansen says:
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It is consistency that tells us that a minus times a minus is a positive, because if it were not, mathematics would be inconsistent[1] and not deterministic.

<snip>

[1] Example of inconsistency

Given that 2 * 2 is 4 and assuming -2 * -2 is -4

a. Then 4 / 2 = 2 (if c = ab then a = c/b and b = c/a, arithmetic)
b. And -4 / -2 = -2 (same reason as above)
c. So far so good, and now we must decide what 2 * -2 is. 4 or -4?
d. If -2 * 2 is 4 then 4 / 2 = -2 (this is inconsistent with a)
e. If -2 * 2 is -4 then -4 / 2 = 2 (this is inconsistent with b)
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More to the point -- your "proof" here isn't good enough.
In your parenthetical "reasons" you are essentially assuming the usual law of signs. That doesn't pass muster if your goal is to prove that no other law of signs is possible.

Cheers,
Joe N

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