  # bloodhound

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Nottingham
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Music, Maths
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Mathematics

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## bloodhound's Achievements 62

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1. 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.
2. Can someone give me an example of a bijection between $\mathbb{R}$ and $[0,1]$
3. 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.
4. Trouble is that there are so many possible divisors of n, I have trouble keeping track of all of them.
5. 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
6. New question: $\sigma_k(n)=\sum_{d|n} d^k$ 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.
7. Define $\Lambda(n):=\log(p)$ if n is a power of a prime p and 0 if n = 1 or n is a composite number Prove that $\Lambda(n)=\sum_{d|n}\mu(\tfrac{n}{d})\log(d)$ The hint says to look at $\sum_{d|n}\Lambda(d)$ and apply the Mobius inversion formula. So far I have got $\sum_{d|n}\Lambda(d)= \sum_{i=1}^r \log(p_i)= \log(\prod_{i=1}^r p_i)$ 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.
8. You aren't allowed to rearrange terms in an alternative series. Don't ask me why :\
9. What? and no Geometric Algebra? That's discrimination I say.
10. 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.
11. 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.
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