# Thread: Properties of the real numbers

1. ## Properties of the real numbers

For a, b in R, prove:
-(-a)=a
(-a)(-b)=ab
-(a/b)=(-a)/b if b is nonzero

how do I even approah this?
For the first one, I have -a+a=0 so -(-a)=a, but that seems way too simple and like it's not doing anything to prove anything. Thank you for any help!

2. Originally Posted by sfitz
For a, b in R, prove:
-(-a)=a
(-a)(-b)=ab
-(a/b)=(-a)/b if b is nonzero

how do I even approah this?
For the first one, I have -a+a=0 so -(-a)=a, but that seems way too simple and like it's not doing anything to prove anything. Thank you for any help!
WE have:

-a + (-(-a)) = 0 and also a + (-a) =0 and from these two equations by using the cancellation law : if a +b = a +c then b =c we get;

a = -(-a).

we also have:

(-a)(-b) = (-1)a(-b) = a((-1)(-b)) = a(-(-b)) = ab ,since (-1)x = -x.

And for the last one we have: =

-(a/b) = -$\displaystyle a\frac{1}{b}$ = (-1)(a$\displaystyle \frac{1}{b}) = (-a)\frac{1}{b}$ = $\displaystyle \frac{-a}{b}$