We will assume .
Since it means for any we can find so that .
We want to show . Let but then . This means by above there is so that . Multiply by to get whenever .
I'm trying to write a delta-epsilon proof that:
I know that exists if such that:
And exists if such that:
I don't understand how I can write a proof using an arbitrary function and limit. So far I have only been proving specific limits with the epsilon delta method, not writing any algebraic proofs like this. Can someone offer some help? Thanks
Edit: I had a thought, but I'm not sure I wrote that second one out right, cause wouldn't I simply have to prove: (which isn't true)?