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As it turns out, that wasn't as bad as I thought it would be. Had some significant time constraints, and some of the concepts of continuity really threw me near the end but it wasn't a total nightmare.

Must admit though, there are still some areas which I feel I still need to "grok". (Hmm... never much liked that word... but replacing it with "understand intuitively" doesn't quite sound right either, but you know what I mean.) Concepts of continuity is one such area that I'll have to spend some extra time on in the revision stage (or maybe even just before my final Analysis section).

In summary, this was certainly the most challenging section yet. Having said that, I did manage to achieve a higher mark than I expected to get in my assignment. As usual, here are some areas in which I screwed up:

It seems intuitive to say that  0 + \infty + 0 = \infty, but this specific rule regarding the sum of these limits was never listed in the set that I can use, so I can't use it, hence I was marked down. I've always enjoyed working with a limited toolset, so this should come naturally after a bit of revision. The main problem is getting that full understanding of the mechanics of each rule so it can become intuitive. In fact, my answer for this particular question (as a consequence) was extremely drawn-out. The proper answer given by my tutor fits on less than half a page of A4. Hopefully more practise will let me see the quick, correct answer more quickly.

I stated Bernoulli's Inequality incorrectly. Absolutely no excuse for that. 🙁

When working out limits of formulas, always state the dominant term before reducing, and always put curly brackets around a sequence (otherwise, it's just a formula).

In some cases I was lazy and claimed that something like \frac{3}{n+2} was a basic null sequence. Although it is quite obviously basic, and quite obviously a null sequence (it converges to 0 as n increases), it's not actually a basic null sequence. So even something as small as this, I need to deconstruct and prove.

Lastly, and this does bear repeating... I need a lot more practise with questions about continuity...

Next up, more group theory!

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