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Wow, that's pretty weird. Thank you anyways.

How do we know to choose δ = ϵ/3? It just came without evidence.

Adding to the above (Carrotstick's working out), it is displaying |f(x) - L| < ϵ implies 0 < |x - c| < δ. So is there an 'iff' implied in the formal definition?

So since all steps are reversible, then |x - 5| < delta implies |f(x) - L| < epsilon?

Thanks for your input Carrotsticks, I follow on what you are saying.

Thanks for your input Shadowdude. I will try it out: Let ϵ > 0, there exists δ > 0 such that for all x in reals and 0 < |x - 5| < δ we have, |(3x-3) - 12| < ϵ Simplifying and collecting like terms, we have |3x - 15| < ϵ Dividing by 3 on each side |x - 5| < ϵ/3 Now, setting δ = ϵ/3...

Is the aim to find a value for delta in terms of epsilon such that is satisfies this 0 < |x - c| < δ implies |f(x) - L| < ϵ condition?

OR what is the most logical, neatest way of laying out such a proof?

Dear BOS members, I would like any immediate assistance on a problem currently at hand, please. Any form of help, which is relevant is much appreciated. Formal definition for limits at a point: Let f be a function defined on an open interval D containing c. Let L be a real number. We...