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Anyone here play ssbb? I haven't played it in years but am feeling like messing around online.

Its usually convenient for it to be.

Re: HSC 2012 Marathon :) $Let $f(x)$:=\begin{cases}0&\mbox{if } x\leq 0\\e^{-1/x}&\mbox{if }x>0.\end{cases}.\\ Sketch $f$. Prove that $f$ is $k$ times differentiable at $0$ with $\frac{d^kf}{dx^k}(0)=0$ for each non-negative integer $k$.$ (This is an example of a smooth function which is zero...

Re: HSC 2012 Marathon :) As others have said...the manipulation is legal BUT it is well beyond a four unit student to justify why. (So I think it is a silly question to ask. All it does is lull more students into the trap of thinking things that LOOK true are true whether or not you can prove...

Re: Complete Guide to 1st Year Uni Do you classify operators on f.d. spaces in this first year course? (Jordan Canonical Form)

Re: Complete Guide to 1st Year Uni Usyd's first year course is devoted to concrete computations mostly from what I remember...things useful for engineers etc to know. Very little is done in the setting of an abstract vector space until second year when we take a deeper look at their structure.

Yes.

Each of the three will observe that the two blue eyed monks they can see do no commit suicide on the second night. Hence all three will deduce they are blue and commit suicide on the third night.

They will see each other alive the next day and deduce that they themselves must have blue eyes. Read the earlier post on the solution in terms of induction.

My view is we DON'T deal with it. I don't see it as an issue that should affect any of my actions/decisions. And just because something can be neither proven nor disproven is no reason to "choose one to believe in." Also I am not sure about your comparison with Heisenberg's uncertainty...

Re: 2012 HSC MX2 Marathon You are right of course cutemouse, I just like to stress the dangers of working backwards as many high school students don't tend to think too much about which directions arguments work. The squaring example is a rather trivial one, but can be well disguised sometimes...

+1

Always sceptical of plausibility arguments...plenty of implausible things happen in this universe. And our very notion of "plausible" is shaped by what we experience.

Re: HSC 2012 Marathon :) Haha how is this anywhere near HSC level? Assuming the integration is counterclockwise, the answer is: I=0 if n is an even non-negative integer I=2*pi*i*nC_{(n+1)/2} if n is an odd non-negative integer.

I am an agnostic atheist. I do not believe in any form of deity, although I can never claim to know with certainty that one does not exist. Nor will I ever condemn others for their personal beliefs. I do not think it makes a difference to the way I should live my life in either case. I think...

Re: 2012 HSC MX2 Marathon Don't need the 'put'. Expand (x^{1/2}-y^{1/2})^2>=0.

Okay, here goes my attempt to explain it. For small numbers of pirates, there is a unique optimal plan for the pirate king to propose (optimal in the sense that it maximises the gold he gets and ensures his survival). I present the first few here for you to get the idea: (100,0), (99,0,1)...

Re: 2012 HSC MX2 Marathon Seconded. Not only does the whole "working from the answer" approach potentially run into logical problems when we try to reverse the argument, (eg. -1=1 (-1)^2=1^2 the final line is true so the first line must be true....WRONG.) this approach moreover kills...

Answer is 456 pirates remaining (I am pretty sure). Sorry for the delay in posting a proof, have been busy doing things around the house. It will be up soon.

The answer is > than all those posted, but nothing silly like 500. I will write a (hopefully!) clear solution in a couple of hours :).