We had to prove this:
Let and be sequences of real numbers. If is bounded and = 0,
then = 0.
(The fact that is bounded is crucial.)
I found this:
My question is where the red arrow is pointing and the red boxed part:
How do I know how to choose 1/M for ε?
In this case we want to prove | | < ε
so I need to choose any ε value right? How do I know to choose 1/M?
Is there algebra I can do that will lead me to choosing 1/M?
I think I understand the rest of the proof up to that point where the red arrow is pointing to.
Any help, suggestions are appreciated. Thanks for your time!