Expert: Vijilant - 2/9/2010

Question
hello  this question is from ordered in realnumber.

if 'a' and 'b' two real number

if a > 0
then -a < 0
proof:-
a > 0
a-a>0-a
0>-a

if a < 0
then -a > 0
proof-
a < 0
a-a<0-a
0<-a

could you please explain the second proof.how  -a can be greater than 0.please explain it

Answer
Hello pratap
I presume you haven't any problem with subtracting a from each side of the equation.
-a is greater than 0 because a is negative.  For example, if a = -3, -a is +3 which is greater than zero.
The other way to see this is to think of the number line. a< 0 means a lies to the left of 0.
If you multiply by -1, that is equivalent to reflecting the number line in 0.  But now, the reflection turns left into right, so -a is to the right of 0.  Which means -a > 0.

Best wishes

vijilant