Mark Allanson
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| posted on 7/10/08 at 09:11 PM |
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You all need to get out more, stop it all NOW and go and get some cars built.
If you can keep you head, whilst all others around you are losing theirs, you are not fully aware of the situation
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liam.mccaffrey
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| posted on 7/10/08 at 09:18 PM |
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right now i have nothing better to do
i (the sqrt of -1) is an imaginary number, and before anyone says "whats the point of imaginary numbers"they are incredibly important in
all sorts of fields like electrical and control engineering
I'm not playing any more
Build Blog
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trikerneil
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| posted on 7/10/08 at 09:22 PM |
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Ooh! imaginary numbers...
That way lie fractals and madness.
Neil
ACE Cafe - Just say No.
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24vseven
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| posted on 7/10/08 at 09:37 PM |
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02GF74
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| posted on 8/10/08 at 10:22 AM |
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Well, I didn't expect 3 pages but we can see it is not that simple an answer.
The best I could come up with was this.
I tried to remember back to school and other than being told "it is the rule", cannot remember if it was ever proved or explained why.
Googling did not come up with anything I was happy with so I thought some more about this.
From my point of view, the problem arises with negative numbers and what they mean in the real world around us. It is not an easy concept to grasp,
and you won’t be alone as remember that one of the most powerful civilisations, the Roman Empire, had no negatvie numbers nor a 0.
In short, negative numbers in the world around us are just nonsense.
For example think of apples.
If you have 6 apples, I ask you how many apples you have, you count them and tell me it is 6.
Now if you have -6 apples, I ask the same question, what do you do? You try to count your apples and then what? You have no apples so do you say 0
since negative apples do not exist?
Clearly something is wrong here.
The explanation given for having a negatvie amount of anything is that you “owe” that number of items and comes into its own when you take a piece of
paper and start to write things down.
Let’s say you owe me 6 apples and have picked 10 apples from the tree in you garden. You decide you want apple pie for supper so sit down to work out
how many apples you can use. You have 10 but owe me 6, the 6 negative apples, which leaves you with 4.
So now it kind of makes more sense.
So back to the original question.
A negative number of something being multiplied a negative number of times? What exactly does “negative number of times” mean in the real world?
Just more nonsense as far as I can see.
But there is a proof. It relies on some simple artithmetic rules which are easier to identify with in the world around us.
a.0 = 0
(-a).b = - a.b
a – a = 0
a.(b + c ) = a.b + a.c
So using the above:
-a.0 = 0
substitute b – b on LHS for 0 gives
-a( b – b ) = 0
expand:
-a.b + x = 0.
x is the result of multiplying two negative numbers: (-a).(-b) which is what we are trying to determine.
For the equation to balance, x must have value a.b
Therefore (-a).(-b) must be equal a.b
Not sure if that is a great proof but the best I can come up with.
It may not make a lot of sense in the real word but keeps mathematics happy.
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