# bloodhound

Senior Members

1996

## Profile Information

• Location
Nottingham
• Interests
Music, Maths
• Favorite Area of Science
Mathematics

• Organism

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62

1. ## Help finding a bijection

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. ## Help finding a bijection

I'll take any for now.
3. ## Help finding a bijection

Can someone give me an example of a bijection between $\mathbb{R}$ and $[0,1]$
4. ## Number Theory : Mobius Inversion

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.
5. ## Number Theory : Mobius Inversion

Trouble is that there are so many possible divisors of n, I have trouble keeping track of all of them.
6. ## Alternating Harmonic Series

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
7. ## Number Theory : Mobius Inversion

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.
8. ## Number Theory : Mobius Inversion

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.

10. ## Alternating Harmonic Series

You aren't allowed to rearrange terms in an alternative series. Don't ask me why :\

12. ## Algebra or Geometry

What? and no Geometric Algebra? That's discrimination I say.
13. ## Easy Graph Theoretical question - HALP!!

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.

15. ## New Internet Explorer

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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