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# Why does -1 x -1 = +1? Watch

1. (Original post by Kabulkid)
haha thanks

cambridge's course is general engineering and imperial is civil engineering, either one would be amazing tbh but still, cambridge is cambridge
Bet your parents are proud of you, cos i surely am and i dont even know you! hahaha.
2. (Original post by scrotgrot)
Plot a square -1 by -1 and measure the area.

Geometry is the key to visualising many non-natural numbers.
But then if you plot a square with measurements 1 by -1 you get positive one as an area?!

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3. (Original post by Numberwang)
Best, easiest and most respectful explanation so far, thanks I love using the double-negative for comic effect, so it's great you used it for comparison
No problem, glad to help

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4. Ours is not to reason why. Ours is but to do and die.
5. (Original post by Afghan Warrior)
Bet your parents are proud of you, cos i surely am and i dont even know you! hahaha.
awww thank you, yeah i guess they are lol

they're buzzing cos they wunna find me a wife soon and cos in our culture education is massive they think as soon as they say 'my son went to cambridge/imperial' girls will be queuing haha.

up until my AS results.. my parents thought im an idiot rofl.
6. Because that's what it says on my calculator
7. (Original post by Kabulkid)
awww thank you, yeah i guess they are lol

they're buzzing cos they wunna find me a wife soon and cos in our culture education is massive they think as soon as they say 'my son went to cambridge/imperial' girls will be queuing haha.

up until my AS results.. my parents thought im an idiot rofl.
Haha I bet they're right about that!! I'd queue up too but then I'd reject you, just to be the odd one out hahaa

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8. Because a transformation of -1 is equivalent to a 180 degree rotation on the number line. Applying that twice gives you the same result, which is multiplication by 1. The same can be shown for any kind of transformation.
9. (Original post by ChaoticButterfly)
Ours is not to reason why. Ours is but to do and die.
10. (Original post by lerjj)
Well done.
11. (Original post by james22)
Doesn't work, plot a 1*-1 square and measure the area.
Yikes, can't believe I missed this
12. Let's assume it was -1

then -1*-1=-1

Dividing by -1 (any number divided by itself =1) gives -1=1 which kind of breaks maths

This is an intuitive explanation, a more formal one can be shown by comsidering the field axioms
13. (Original post by Arithmeticae)
Let's assume it was -1

then -1*-1=-1

Dividing by -1 (any number divided by itself =1) gives -1=1 which kind of breaks maths

This is an intuitive explanation, a more formal one can be shown by comsidering the field axioms
The issue is that this only works to disprove (-1)(-1)=(-1)
Maybe it's 3? Or Pi? And we can't test them in the same way, because I'm pretty sure dividing by (-1) requires previously defining multiplication by it, so you're not allowed to do that.

It's hard to know how much we're working with here. I think we're trying to define any form of multiplication by negatives (including their reciprocals).
14. idk...i end up accepting most of maths without understanding it
15. As I said before, its just a quick intuitive explanation, but if you want to get really picky about it...

(−a)b+ab=(−a)b+ab

(−a)b+ab=b(a−a)

(−a)b+ab=b(0)

(−a)b+ab=0

(−a)b=−ab

(−a)(−b)+(−ab)=(−a)(−b )+(−a)b

(−a)(−b)+(−ab)=(−a)(b− b)

(−a)(−b)+(−ab)=(−a)(0)

(−a)(−b)+(−ab)=0

(−a)(−b)=ab

although it should be pretty clear it's not going to be something like 400 :/

(Original post by lerjj)
The issue is that this only works to disprove (-1)(-1)=(-1)
Maybe it's 3? Or Pi? And we can't test them in the same way, because I'm pretty sure dividing by (-1) requires previously defining multiplication by it, so you're not allowed to do that.

It's hard to know how much we're working with here. I think we're trying to define any form of multiplication by negatives (including their reciprocals)
16. (Original post by Arithmeticae)
As I said before, its just a quick intuitive explanation, but if you want to get really picky about it...

(−a)b+ab=(−a)b+ab

(−a)b+ab=b(a−a)

(−a)b+ab=b(0)

(−a)b+ab=0

(−a)b=−ab

(−a)(−b)+(−ab)=(−a)(−b )+(−a)b

(−a)(−b)+(−ab)=(−a)(b− b)

(−a)(−b)+(−ab)=(−a)(0)

(−a)(−b)+(−ab)=0

(−a)(−b)=ab

although it should be pretty clear it's not going to be something like 400 :/
I said 500, because chaos butterfly quoted Charge of the Light Brigade.
17. "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."- Bertand Russell

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18. Didn't this topic get posted around a month back, it became quite a massive thread as far as I remember.

Couldn't find it, but found this slightly older one if you want to have a look.
http://www.thestudentroom.co.uk/show....php?t=1027293
19. (Original post by Afghan Warrior)
Haha I bet they're right about that!! I'd queue up too but then I'd reject you, just to be the odd one out hahaa

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lol awww... what if you're the only one i like out of them
20. (Original post by Kabulkid)
lol awww... what if you're the only one i like out of them
well you'll have to prove that then wouldnt you

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