Honestly these sections are still like Hebrew to me. I don't have a real concrete understanding of the general format to prove limits; I scooted by just barely in the last homework. Choosing the epsilon/sigma always throws me. I'm sure I'll get it, but as of right now it's my biggest obstacle to mastering these sections. One thing that doesn't make sense to me is the necessity of condition 2 for continuity when we have condition 3. Is there ever a time when condition 3 (on page 289) is satisfied when condition 2 isn't?
I enjoyed the proofs that were showing the addition of two things (whether they be polynomial or just general functions) have the same limit as that of the individual limits added together. The same also goes for the product of two objects. The use of inequality amazes me. It seriously is like the best thing in a proof. You can typically make something smaller (or larger) that makes your proof not only possible but ten times as simple.
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