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But I don't see why we need the requirement: a number system must be a division algebra?

And isn't dimension dependant on the field you're working over? For example, the complex numbers are a one dimensional algebra over themselves, but a two dimensional algebra over the reals. Either way, I don't think dimension is a useful property to try and attach to the concept of number. I'm...

Why are you associating division algebra with the word number? Surely you consider the natural numbers to be numbers? I'm with Cayley and Dickson on this one.

I don't see why. The derivative is undefined at x = 0 because the function is undefined for x < 0, but that doesn't mean there is going to be a vertical tangent there. In fact, given the derivative he listed, my guess is the function has a tangent line whose slope is very close to 3 when you're...

Is it just me, or is that red building fuggin ugly? Obligatory link

jb_nc is a BoS snob :)

BIT is going to be light on the problem solving and heavy on the "English" side of things, but if business was your favourite subject in the HSC then maybe this is your thing. If solving problems was really your thing, then obviously engineering.

Better to just get a feel for how multiplying by 'x' changes a graph imo. Doing it pointwise like that without a feeling might be time consuming for no reason.

Did anyone else find the ACA / Crisco thing a bit sickening? I mean, it would have been fine if it didn't reek of a 10-minute commercial for Crisco, but as it was presented it felt like they weren't doing it to help people at all.

What courses did you do during your HSC, how do you rate them, and why do you rate them that way?

You know what the graph for sqrt(x) looks like, right? Well, this thing will be the same basic shape, just increasing quicker. To get your bearings for this one as opposed to sqrt(x), this thing still starts at (0,0), but passes through (1, 4) and (4, 20) instead of (1,1) and (4, 2). Same shape...

I'm pretty sure you can't do this any more. UGrad + Master of Teaching now.

You're studying maths down at ANU? How is it?

Re: Parramatta council fights against jews with "merry christmas" signs. We have a winner.

Re: Parramatta council fights against jews with "merry christmas" signs. If people are too stupid to ascribe their own meanings to the holiday (yes, I used the h word) independently of the terminology associated with the holiday, they're too fucking stupid to be listened to by local councillors...

Why do you think Ngô Bảo Châu will win it? Because everyone else thinks he will win it, or because you have enough of a feeling for the maths the "contenders" are doing to be able to judge? Personally, I can't make heads or tails of the maths these guys are into so I have no idea who deserves...

addikaye03 gave them in his last line.

Ahh, too quick for me :) P.S. pi isn't rational.

The paddock has a radius rp given by: A = \pi r_p^2 \Rightarrow 1 = \pi r_p^2 \Rightarrow r_p = \frac{1}{\sqrt{\pi}}. Now, you want the goat to eat half a square unit of grass, or equivalently, to leave half a square unit of grass uneaten. Assuming the goat can traverse the entire...

Please explain.