If a and b are postive numbers. a < b then 1/a > 1/b. Prove Lemma.?

Question

posted this once before but forgot to note that a and b are POSITIVE. need to prove that if 0 or < im assuming[>] ) 1/b.

so if a 1/b.

my mistake, i didnt know how to add details until now.
thanks for the heads up.

Answer 1

Given: a, b>0, a
a ca < cb, if c > 0

Use c = 1/(ab)
a/(ab) < b/(ab)
1/b < 1/a

Q.E.D.


It all relies on ca < cb, if c > 0 being true. Here's how you prove that.

a a+d = b
ca+cd = cb

Since there is a positive number (cd) such that cb = ca + cd, cb > ca.

Q.E.D.

Answer 2

1/a < 1/b ? // Multiply both sides by ab

Because a and b are positive, so is ab:
ab/a < ab/b ??

b < a ? No! a>b, Thus 1/a < 1/b is not true.

Answer 3

There really was no need for you to delete the previous question after people took the time to answer it. All you had to do was add the additional details.