such that whenever it follows that .
Looking at the latter expression and noting that a > 0:
So what should we choose?
What don't you understand?
Here's the formal definition of a limit:
such that whenever it follows that
Here: and .
With these epsilon-delta proofs, we play around with the expression to get for some .
Why do we do this? Because we know that . So if we let , then through all the algebra we did, it must necessarily follow that .
By definition, this proves that