# Limits Proof

Hello,
given lim(an)=a and lim(bn)=b if a<b prove that an < bn.

can i say that if a/b < 1 than an<bn ?

What if b = 0?

if b=0 than a is negative and probably an < bn
so it still holds, but how do i prove that?

can I say that
lim(an-bn) = (a-b) < 0
hence an < bn ?

You can, but it doesn't convince me that an < bn. Also, I think that what you're trying to prove is false.

HallsofIvy
Homework Helper
Hello,
You can't prove it- it isn't true. What you can prove is that for n large enough, an< bn. Use the definition of limit with $\epsilon$ less that half the difference between a and b.