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Message Board > Malarkey > Simple subtraction question

April 15, 2013, 17:27
Zomg
None
641 posts
On a number line, when you subtract, you go to the left from 0. When you add, you go to the right from zero. But when you do e.g. 8- -2, how do you move -2 places? Why does - - result in +?

While any valid answer is welcome, I would much prefer answers in the style of ontological proofs:
http://www.scribd.com/doc/6194 … Complex-Numbers

Thank you.
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April 17, 2013, 14:05
Dennis
どこかにいる
2050 posts

Substracting is just adding negative numbers.

5-2 = 5+(-2)

a "-" as a sign could also be seen as "-1 times"

-5 = (-1)*5

a "-" as operator could be seen as "adding -1 times"


5-2 = 5+ ((-1)*2)


Agreeing on that you can do this:

8-(-2) = 8 + ((-1)*(-1)*2) <=>
8-(-2) = 8 + ((-1)*(-1)*2) <=>
8-(-2) = 8 + (1*2) <=>
8-(-2) = 8 + (1*2) <=>
8-(-2) = 8 + (2) <=>
8-(-2) = 8 + 2 <=>
8-(-2) = 10

[Edited on April 17, 2013 by Dennis]
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Kwakkel
#
April 17, 2013, 14:18
Dennis
どこかにいる
2050 posts

Be aware that there is a difference between "-" as an operator and "-" as a sign. The sign just tells something about the number (it's minus 5 degrees) meaning it is lower than zero.

It isn't that special because if I added a number to each term in the equation the result wouldn't change.

10-5 = 5

add 20

30-25 = 5


add 1

11-6 = 5

add 1000

1010 - 1005 = 5


the result will never change no matter wht you add to both terms.

x = 8-(-2)

x = (8+10)-((-2)+10) //I add 10 to both terms

x = (18) - (8)

x = 10
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Kwakkel
#
April 17, 2013, 17:21
Zomg
None
641 posts
Very nice work Dennis.. I guess those mathematics hours at high school paid off huh? :o

What does <=> mean? "if and only if"?

Dennis, could you please tell me if this is correct:

http://www.youtube.com/watch?v=oZ8S0--fj8g

Zank yuu.
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April 18, 2013, 10:54
Dennis
どこかにいる
2050 posts

lol @ hax00rify

It seems correct.

it means "if and only if"
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Kwakkel
#
April 18, 2013, 11:00
Zomg
None
641 posts
hax00rify is my clandestine account I use for uploading videos to show to people (strangers) on the internet (I know you're not a stranger but yeah =P) so that they can't track who I am.

I posted that video on some other forums as well. =)
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Message Board > Malarkey > Simple subtraction question

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