Lose the brackets.

Essentially, yes.Now, epsilon is just some small number that represents how far away the sequence is from the limit.

No, it is any value which makes not LESS than epsilon, but makes the distance between the limit and the sequences less than epsilon. In fact, it is most often taken to be the least value for which this is true.When we find a value for we have the largest possible value for which the sequence is less than epsilon.

Once again it's the distance between teh limit and the sequence which is less than epsilon.For every the sequence will be less than epsilon and so we can write .