Search results

man.. isn't that mathematical enough for you? :P I could write out my first proof in terms of group theory/algebra. But that's not that helpful.. Case 1): You want a formal mathematical refutation of the claim that ln(-1)=0. In that case, suppose the statement were true. raise both sides to the...

Basically, ln is defined as the inverse function to e^x. As such, its domain is all positive reals, and ln(-1) is hence an invalid function. Some might like to counter this by saying "but aha! What about e^ix = cos x + i sin x"? Well, in that argument, you could indeed get ln(-1). But this...

I guess the main thing you missed there was algebra. This involves group theory, rings and stuff like that with elegant symbols and almost no real numbers... :) well, parts of it can do that anyway. And, if you put in stats as a subsection of mathematics, you should probably include applied...

I got 119 I think... I didn't do much work. But then, I learnt it back in year 10, and i was doing olympiad stuff for most of year 12. You SHOULD try to do papers - they help. So don't take me as an example.. EDIT: I think justchillin has the right approach. First 4 questions - make sure you...

I reckon it's pretty stupid... mark inefficient... if you hit your peak in the middle of the exam you SHOULD be doing 4,5,6 for most people anyway. Because you get a lot more marks on average from 4,5,6 - the doable-but-tricky questions - than 7,8 the questions which everyone assumes they can do...

we're like pieces of nostalgia you get every so often... we pop up for a second, then you blink and we're gone again :P

man.. no one learnt anything from my recursions lectures did they..

however, you probably can't assume cauchy anyway. Because it's nowhere near the reach of the syllabus you'd probably have to prove it (2 pages+) in order to use it.. The AM-GM is useful, and probably the only thing (short of them guiding you through something) that you'll need for 4U.

I know the first one... busy right now, but if no one posts within a day bump it and I'll post up. Second one: Think about later. Ohh.. I'm assuming you don't know the answer.. if you do, get cracking on it guys who read these posts! :)

basically, just writing a number as the product of prime numbers. So for example, 24 is not a prime number. but we can divide out by 2 to get 12, again by 2 twice to get 3 and by 3 to get 1 so 24 = 2^3*3. Similarly 120=2^2*3*5. Note that all the things which are raised to powers (here 2,3 and...

Umm... ok. So n^3=m^5. Let n=p1^a1*p2^a2*p3^a3.....*pn^an. (too lazy... you know a1 is a subscript 1 etc) Obviously m has to have the same factors... so m=p1^b1*p2^b2*...*pn^bn. n^3=p1^3a1*p2^3a2*p3^3a3.....*pn^3an. m^5=p1^5b1*p2^5b2*...*pn^5bn. So because the two numbers are the...

If you split n up using prime decomposition you will see that n has to be a power of 5. Therefore take 5th root of 3000000 - floor of that number should be possible values of (5th root of n) and hence the possible number of values n can take. This is the same as the number of values m can take...

as far as I know, no.

you mean the specific form of the cauchy inequality, otherwise known as the AM-GM? :)

closed. This is getting really unproductive..

A shorter version of what I wrote before: (0(00)*(10+01)(00)*(10+01)(01*0+1)*)+(1(00)*(10+01)(01*0+1)*) I know it's still longer than their answer but I understand how it works: the (10+01) is brilliant. It allows you to put in a 1 no matter the parity of 0's before it and preserve the...

lol... and you thought that one was short? Umm.. I think that + in your one means "or" right? In that case, I think that 0 is a valid string (take none of first, none of last, and the 0 in the middle one)... which is dodgy...

hmm. I just learnt about regular expressions :) http://www.cs.princeton.edu/introcs/72regular/ it's from princeton so it can't be that far off.. After thinking about this for a few minutes, I think that the answer IS quite ugly. For firstly you want to try to get rid of the at least two 1's...

Umm, this isn't a uni assignment is it? is it worth marks? I know the answer, I can describe it to you,but if you have a definition of "regular expression" that'd be nice..

hehe... the apology was aimed at you mostly I guess. But I guess I'm too competitive... I've done quite a few olympiad questions involving manipulation of strings etc, but if you're thinking about the more programming side of things, I'm not that sure... post up the question, if I don't know...