

bloodhound
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62 ExcellentAbout bloodhound
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Nottingham
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Music, Maths
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Mathematics
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Thanks a lot! I must warn you that I will probably swamp this board with questions on Algebra and Topological spaces in the coming days. Meanwhile, I'll go read up on the cantor schroeder bernstein theorem. I just hope it's not too complicated.
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I'll take any for now.
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Can someone give me an example of a bijection between [math]\mathbb{R}[/math] and [math][0,1][/math]
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Yep, I figured it out. I didn't realise sigma k was just sum of divisor function for k=1 for which we have already done the formula.
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Trouble is that there are so many possible divisors of n, I have trouble keeping track of all of them.
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from my first year lecture notes from a random lecture note from internet Still doesn't explain why though :\, I guess I'll have to google it up. edit: some links that might help you http://ecademy.agnesscott.edu/~lriddle/series/rearrang.pdf http://personal.denison.edu/~feil/classes/Rearrangement.pdf
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New question: [math]\sigma_k(n)=\sum_{d|n} d^k[/math] It was asked to show that sigma is multiplicative, which I have done. I have to find a formula for it which is where I am stuck.
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Define [math]\Lambda(n):=\log(p)[/math] if n is a power of a prime p and 0 if n = 1 or n is a composite number Prove that [math]\Lambda(n)=\sum_{d|n}\mu(\tfrac{n}{d})\log(d)[/math] The hint says to look at [math]\sum_{d|n}\Lambda(d)[/math] and apply the Mobius inversion formula. So far I have got [math]\sum_{d|n}\Lambda(d)= \sum_{i=1}^r \log(p_i)= \log(\prod_{i=1}^r p_i)[/math] assuming that n has r distinct primes in its expansion. So help Don't mind the above, I have figured it out. I will post more questions if any in this thread instead.
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You aren't allowed to rearrange terms in an alternative series. Don't ask me why :\
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What? and no Geometric Algebra? That's discrimination I say.
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First question of the first exercise sheet from my graph theory course, and I'm just stuck. Maybe I am not thinking right. Any hints are welcome Questions: Show that in any group of 6 people, either there are 3, each one of whom knows the other two, or there are 3 people none of whom knows the other two.
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talking about sp2, it limits the number max number of outbound connections attempts per second from infinity (almost) to 10. You can still use a patch to change it back, cos that might affect the performance of swarm p2p like bittorrent.