MoogleViper Posted November 11, 2009 Posted November 11, 2009 I couldn't find the old thread so I'll start a new one. Prove that when m and n are integers, n is always a multiple of 6. n=m³-m
Iun Posted November 11, 2009 Posted November 11, 2009 I couldn't find the old thread so I'll start a new one. Prove that when m and n are integers, n is always a multiple of 6. n=m³-m ... You know what's more fun than maths? Girls! Girls and their vaginas! But in the spirit of learning, I'm going to answer your question with a question: "Prove that when your degree is higher maths, that finding integers, indices, rationals and irrationals is going to get you a hot wife"
EEVILMURRAY Posted November 11, 2009 Posted November 11, 2009 Go see the Wizard of Oz. Scarecrow did fuck all study but he got a diploma.
chairdriver Posted November 11, 2009 Posted November 11, 2009 n = m^3 - m n = m (m^2 -1) By difference of two squares: n = m(m+1)(m-1) Thus either m+1, m or m-1 must be a multiple of 3, since they are three consecutive integers. And one of the three will always be an even number, ie. a multiple of 2. Thus; n = a.2b.3c where a,b,c are arbitrary integers. Therefore n = 6d, where d is again an arbitrary integer. Hence n is always a multiple of 6. Done, and dusted, so well.
Mr_Odwin Posted November 11, 2009 Posted November 11, 2009 n = m^3 - mn = m (m^2 -1) By difference of two squares: n = m(m+1)(m-1) Thus either m+1, m or m-1 must be a multiple of 3, since they are three consecutive integers. And one of the three will always be an even number, ie. a multiple of 2. Thus; n = a.2b.3c where a,b,c are arbitrary integers. Therefore n = 6d, where d is again an arbitrary integer. Hence n is always a multiple of 6. Done, and dusted, so well. Nice. I immediately thought of proof by induction but your method is so much more concise. Proof by induction: Works for 2? 2^3-2 = 6. Yes. Works for 3? 3^3-3 = 24. Yes. Inductive leap. Assume works for k, an arbitrary integer: k^3-k. Yes. Then for k+1: (k+1)^3 -(k+1) = ... = (k^3-k) +3k(k+1) We know k^3-k is divisible by 6. k(k+1) must be an even number times by an odd number which is even so 3k(k+1) must be divisible by 6 also.
Supergrunch Posted November 11, 2009 Posted November 11, 2009 Chair's method for the win I think, if he wanted girls it'd get him them. :wink:
Mr_Odwin Posted November 11, 2009 Posted November 11, 2009 Chair's method for the win I think, if he wanted girls it'd get him them. :wink: Attracted by the maths, repelled (in the nicest possible way) by the blatant homosexuality. :p
chairdriver Posted November 11, 2009 Posted November 11, 2009 Attracted by the maths, repelled (in the nicest possible way) by the blatant homosexuality. :p Although, She loves it.
MoogleViper Posted November 11, 2009 Author Posted November 11, 2009 A big thank you to you good sir.
EEVILMURRAY Posted November 11, 2009 Posted November 11, 2009 She loves it. You seem to be enjoying it ALOT more. Out of shot strap-on perhaps?
jayseven Posted November 11, 2009 Posted November 11, 2009 So who wants to do my homework for me? Do a word-association experiment to see how your subjects' mental lexicons are organised. Actually I might just do it myself - it seems quite fun.
Mr-Paul Posted November 11, 2009 Posted November 11, 2009 Anyone feel like discussing whether there is a distinct conservative ideology? I don't. Blahpolitcscrappppp
Molly Posted November 11, 2009 Posted November 11, 2009 Chair's method for the win I think, if he wanted girls it'd get him them. :wink: It really would!
Haden Posted November 11, 2009 Posted November 11, 2009 (edited) Anyone feel like discussing whether there is a distinct conservative ideology? I don't. Blahpolitcscrappppp Check out English philosophers and politicians in the aftermath of the French Revolution. Espcially this guy http://en.wikipedia.org/wiki/Edmund_Burke Then later as the floodgates for an increased electorate opened. Disraeli will be very useful for this bit. He appealed to Conservatism being the natural party of the people compared to narrow elitist liberal interests. Something Michael Howard did rallying against mass immigration in defence of a threat to the white working class. Maybe bring in aspects of Majors back to basics vision of a past Green England which is being mirrored by Sarkozy in France atm. You could have fun with this essay talking about splits of conservatism Ron Paul and John McCain for example. I mean Fox news probably hate Ron Paul a Republican Candidate more than some of the Democrat ones! Basically Conservatives who believe in the good influence of American interventionist power and hard patriotism vs isolationist look after ourselves first type of Conservative. Also maybe talk about how when a national institution reaches a certain point of history and penetrates the national character maybe a generation or so. The Tories who may have once opposed it now say they are the natural party to look after it. http://news.bbc.co.uk/1/hi/8210977.stm Sorry a real incoherent ramble there. Hope its a tiny bit of use. Edited November 11, 2009 by Haden
Mr-Paul Posted November 11, 2009 Posted November 11, 2009 Thanks, I was trying to write in a way where i was presenting arguments for there being a distinct ideology, then arguments against it, but I found that didn't really work. i'm trying to restart it by showing how the Tory party started out and the influence of Burke and Disraeli and going on from there, linking it back to them and 'One nation' conservatism where applicable but also providing contrast when it comes to Maggie Thatcher's more neoliberal approach and debates in the party today on which way they're going. Meh, I think I know more about it than I think I do, it's just quite hard getting it down into a coherent essay! It kinda sucks when all the books that I've got out are prettty useless or too confusing and wikipedia is the best source (which we can't reference at all!)
Ten10 Posted November 12, 2009 Posted November 12, 2009 For anything maths related, from now on just use bing. Documentation Now powered by wolfram Alpha
Mr_Odwin Posted November 12, 2009 Posted November 12, 2009 For anything maths related, from now on just use bing. Documentation Now powered by wolfram Alpha Wolfram Alpha, although powerful enough, is nowhere near the level needed to provide a mathematical proof like the ones above. It lacks intuition, which is often needed.
Cube Posted November 12, 2009 Posted November 12, 2009 Wolfram Alpha, although powerful enough, is nowhere near the level needed to provide a mathematical proof like the ones above. It lacks intuition, which is often needed. Plus, the steps towards the answer are usually more important than the answer.
chairdriver Posted November 12, 2009 Posted November 12, 2009 Can someone help me with: Use the binomial theorem to show that (1 + 2/(n^1/2))^n >= n for n >= 1 (>= is "greater than or equal to")
EEVILMURRAY Posted November 12, 2009 Posted November 12, 2009 Nice. I immediately thought of proof by induction but your method is so much more concise. Proof by induction: Works for 2? 2^3-2 = 6. Yes. Works for 3? 3^3-3 = 24. Yes. Inductive leap. Assume works for k, an arbitrary integer: k^3-k. Yes. Then for k+1: (k+1)^3 -(k+1) = ... = (k^3-k) +3k(k+1) We know k^3-k is divisible by 6. k(k+1) must be an even number times by an odd number which is even so 3k(k+1) must be divisible by 6 also. I don't think I ever came across "^", what does it signify?
chairdriver Posted November 12, 2009 Posted November 12, 2009 I don't think I ever came across "^", what does it signify? Normally in maths it signifies the vector cross product, and it's often pronounced "vec". http://en.wikipedia.org/wiki/Cross_product However, here it's used to denote powers, because there's no easy way to do superscripts in a forum environment. 3^2 = 3x3 = 9
Nintendohnut Posted November 12, 2009 Posted November 12, 2009 Ah man it's really cute/cool that what used to be a 'help with my homework!' thread has now become a Uni based one as all the aficionados grow up and move away I think its awesome that we've kind of all grown up together as a part of this community and shizzle. Anyway, as I do English Lit there isn't much help you guys can give me short of physically writing essays for me but at least I know you're here if I did ever need that :p
Dannyboy-the-Dane Posted November 12, 2009 Posted November 12, 2009 Ah man it's really cute/cool that what used to be a 'help with my homework!' thread has now become a Uni based one as all the aficionados grow up and move away I think its awesome that we've kind of all grown up together as a part of this community and shizzle. Anyway, as I do English Lit there isn't much help you guys can give me short of physically writing essays for me but at least I know you're here if I did ever need that :p I'm still in high school for a year! >_<'
Calza Posted November 12, 2009 Posted November 12, 2009 I've been struggling with this essay for weeks now, what are your guys tips for actually writing a good solid essay? It's on digital rights management and the question just seems out of date which is really rather annoying.
Will Posted November 13, 2009 Posted November 13, 2009 When I was at uni I would write my essays like this: 1. A little reading around the subject (this stage didn't often happen) 2. Decide on my conclusion. 3. Bullet point each thing I want to cover, making sure the first leads through nicely to the conclusion. 4. Flesh out the bullet points. Which should leave you with a pretty much completed essay. I guess you might also read through it at the end to make sure it makes sense. I never bothered though.
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