If we can agree that a negative number is just a positive number multiplied by 1, then we can always write the product of two negative numbers this way:
(a)(b) = (1)(a)(1)(b) = (1)(1)ab
For example,
2 * 3 = (1)(2)(1)(3)
= (1)(1)(2)(3)
= (1)(1) * 6
So the real question is,
(1)(1) = ?
and the answer is that the following convention has been adopted:
(1)(1) = +1
This convention has been adopted for the simple reason that any other convention would cause something to break.
For example, if we adopted the convention that (1)(1) = 1, the distributive property of multiplication wouldn't work for negative numbers:
(1)(1 + 1) = (1)(1) + (1)(1)
(1)(0) = 1 + 1
0 = 2
As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."
Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (1)(1) = +1.
http://mathforum.org/dr.math/...
Why does a double negative equal a positive, but two positives don't equal a negative?
Moose
2009/04/25 19:19:51


10 votes


38%  
2 votes


8%  
5 votes


19%  
1 vote


4%  
4 votes


15%  
4 votes


15% 
And Why don't two wrongs make a right?
Top Opinion

Zuggi 2009/04/25 19:26:47Because...
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Fun
2014/09/02 23:04:44
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Inquiring minds want to know.
Yeah, Right...
and 2 wrongs dont make a right because the overly protective parents of our corrupt country said so
"No, I walked." would be an example of a negative answer to the question "Did you run to school today?"
Also, two negatives may mean a negative still.
"No, I did not run."
But, the teacher said to her class, two positives are never joined to mean a negative.
To which little Johhny shouted "YEAH, RIGHT!"
Like if you say "I cannot not do that," you are really saying "I can do that" because if you can't not do something that means you can do it...
Two wrongs might not make a right...but two rights do make a left.
(a)(b) = (1)(a)(1)(b) = (1)(1)ab
For example,
2 * 3 = (1)(2)(1)(3)
= (1)(1)(2)(3)
= (1)(1) * 6
So the real question is,
(1)(1) = ?
and the answer is that the following convention has been adopted:
(1)(1) = +1
This convention has been adopted for the simple reason that any other convention would cause something to break.
For example, if we adopted the convention that (1)(1) = 1, the distributive property of multiplication wouldn't work for negative numbers:
(1)(1 + 1) = (1)(1) + (1)(1)
(1)(0) = 1 + 1
0 = 2
As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."
Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (1)(1) = +1.
http://mathforum.org/dr.math/...