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  • Your wording is a little confusing but if I interpreted your question correctly then the answer is yes:

    One could use a technique similar to induction to prove a proposition about all integers by showing that S(0) is true, and then showing that:
    S(n+1) is true whenever S(n) is true.
    S(n-1) is true whenever S(n) is.

    From this we can conclude that S(n) is true for all integers n.
    (All we are really doing is applying induction twice separately.)

    In fact induction as you know it can be adapted to any set of the same "size" as the positive integers. You have probably already seen this when you have proven things about all EVEN integers say.
    Well everyone said to me stuff like hold on and you'll have a back up and stuff like that, so I went through the year with 12 units, but I kinda knew from the start that if anything wasn't going to count it would be eco. So now come HSC i've still got 12 units (I know you've got 14 so its even more) and even though im rank 1 in economics, I haven't studied for it because I know that it won't count over my other subjects cos I'm better at them.

    So i reckon just start the year with everything and as it progresses you will realise what are your strengths and everything will sort itself out and then just drop accordingly.

    and then toddle off and do combined med at USyd all sweet ;)
    I like to think so lol, even though I still make silly mistakes like a bitch.

    not from a marks standpoint, but from an understanding point I think I am much better at 4u than 3u. <-- that may sound very strange

    state rank is the dream for me too haha, but my temperament in maths tests is quite poor so it all depends on the day. I think I have a much better chance in either physics or chem really. Are you dropping one of your subs into next year?
    I reckon u can do it. but anyway it will set you up hardcore for 4u which is where you really want to shine :) I remember going into the exams last year I was so confident, but then I absolutely got smashed by the 3u and I realised how limited my knowledge actually was, so this year 4u was so much clearer because I had already gone through 3u and it all just clicked.
    haha nah respect for that post, when that chick was quoting fiction novels and dramatic films I was shaking my head.

    but if she tops herself you're to blame... loljks
    Haha I did a creative. There wasnt really a topic, u can do what u want. I chose to explore concepts of reality, perception and the nietzschean superman
    I'll be attempting the 2012 paper, but not officially. That is, I will still be doing it under exam conditions, but no official mark.
    Definitely not annoying, its good that you think about this sort of thing carefully!

    I suppose from a HS point of view that can be taken as the definition of pi, although there are issues with this: namely that things like arc length and hence circumference are not properly defined (some kind of integration is needed to give a notion of arc length.) Also the approach to trig functions is pretty nonrigorous.

    I would think that a cleaner way to define pi without appealing to geometry (because the axioms of geometry are rather subtle and complicated) is defining the sine function by its convergent Maclaurin series and letting pi be its smallest positive root. Every property of pi should fall out from this.
    No worries- and lol I legit meant it. You're easily the best 3U kid on this forum (we were actually talking about you during the BOS trials and talking about that) so yeah- I've got faith in you. Just do your best and you'll rape it :)
    Im just gunna ask in 10 minutes and still do it properly. Im sure he will trust us either way if we say that we did it properly
    Carrot said 11 on the last page of the thread, but hopefully he messages the test earlier because I want to print it off properly with booklets etc.
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