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## Main Question or Discussion Point

I understand most of the logic behind the formal definition of a limit, but I don't understand the the logic behind an epsilon delta proof. The parts I'm having trouble with are these:

1. How does proving that, the distance between the function and the limit is less than epsilon whenever the distance between x and a certain x value less than delta?

2. How does reducing the epsilon side absolute value equation to mirror the delta side absolute value equation give us delta? (As inarticulate as that sounds, I can't word it any other way)

Thank you for your help!

1. How does proving that, the distance between the function and the limit is less than epsilon whenever the distance between x and a certain x value less than delta?

2. How does reducing the epsilon side absolute value equation to mirror the delta side absolute value equation give us delta? (As inarticulate as that sounds, I can't word it any other way)

Thank you for your help!