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Proof That Multiplying Two Negatives Numbers Gives You A Positive One

Posted by judgmentoftherain

One of the most enjoyable things in the world can be a simple proof. 

prove that 

(-1)(-1)=1. 

Now, how would we go about doing this exactly?

First,

0=-1(0). This reads zero is equal to negative one times zero. In other words, on the right hand side we have no negative 1s. 

Second, 

0=-1(1-1). 1 minus 1 has the same value as zero. 

Third, use distribution. 

0=-1+(-1)(-1). One times a negative one is a negative value. Another way of putting this is that we have 1 negative 1 value. 

Fourth, add one on both sides of the equation.

1=-1+1+(-1)(-1)

Fifth, since -1+1 is equal to zero, we have

1=0+(-1)(-1). 

Sixth, because 0+a=a, we now have

1=(-1)(-1). 

https://www.youtube.com/watch?v=-YCN-a0NsNk

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Comments

Posted by judgmentoftherain

Oh and one last thing...I promise. When I'm referring to numbers, I mean real numbers. Complex numbers are a different story entirely. For those who don't know, i=square root of negative one. I is considered a complex number, which is not a real number. If we did (-i)(-i), we would not get a positive number. Instead, we get (-i)(-i)=-1. Sorry for not defining my terms a bit better.

Posted by judgmentoftherain

Some really needs to allow editing on this website, so that goofballs like me can fix their mistakes lol.

Posted by judgmentoftherain

Also, in step 4 it should read. 1+0=-1+1+(-1)(-1) Step 5 should say 1+0=0+(-1)(-1)

Posted by judgmentoftherain

Sigh.... Correction: Proof That Multiplying Two Negative* Numbers Gives You A Positive One.