Homework Sourse23 Show that if a 0 then a b SolutionAnswer If a b for ev
23. Show that if a 0, then a b. 
Solution
Answer :
If a < b + for every > 0 then we show that a b
For a contradiction let us assume a > b then a - b > 0
Let s = a - b > 0
Consider b + (s/2) = b + ( a - b ) /2 = ( a + b)/2 < ( a + a )/2 = a
Since s > 0 , so that = s/2 > 0 , so for a positive real number , we have a > b +
which is a contradiction to our assumption \"a < b + for every > 0\"
Hence , if a < b + for every > 0 then a b
