# river_rat

Members

29

• #### Last visited

• Birthday 07/21/1983

## Profile Information

• Location
South Africa
• Interests
• College Major/Degree
Mathematics
• Favorite Area of Science
Semigroup Topologies
• Occupation
Teaching Assistant

• Quark

10

1. ## Something Summation

You cannot find the roots of a general polynomial of degree $\geq 5$ if you limit yourself to addition, multiplication and taking square roots Atheist. I guess that is what you meant by analytical, as there are other analytical solutions if you allow other operations and functions, like the elliptic functions for the quintic case.
2. ## integral, and some other stuff

I'm surprised no one chastised me for my solution - oh well
3. ## Interesting identity

Hi abskebabs Here is a big hint for you - how do you factor $a^n - b^n$?
4. ## Interesting identity

Hey abskebabs You can do one better then what you have posted so far: if $2^n - 1$ is a prime number then $n$ must be prime. I'll leave the proof up to you, its not difficult
5. ## Impossible Brain Teaser?

The problem is impossible to solve - Dr Math has a nice solution http://mathforum.org/dr.math/faq/faq.3utilities.html
6. ## integral, and some other stuff

or if you feel daring, your answer is $\Im \left( \int e^{(2+3i) x} dx \right)$ which saves you all the product rule pain PS $\Im$ denotes the imaginary part if you are wondering. The $dx$ is called a differential form (or one form in this case) and the theory here is quite interesting. It takes a surprising amount of mathematical work to get something that is more meaningful then the nonsense idea of an infinitely small but non-zero change in x.
7. ## Need book recommendation for stochastic processes

I would suggest "Probability and Random Processes", by Grimmett I think, for a quick and easy intro to the basics here. Its nice, starting with the basics and ending with the Ito calculus.
8. ## Apparently equilivant series.

How is the second recurrence well defined tree?
9. ## Find the value of x in this equation:

Ah, but that is a different question. I only stated i could extend the algebraic operation of addition to a larger set that includes some ideal points. To start talking about limits you must have introduced a topology. To talk about limits and addition it would be nice if addition was continuous with respect to this topology. Now if you want a "nice" topological extension of the reals i would have to suggest the Stone-Cech compactification where addition can be extended by the universal property of that compactification. Sadly I think we only get an operator which is left continuous but we are still better equipped to talk about limits here. Well share the sketch
10. ## Find the value of x in this equation:

But you have not explained why we are limited to group operations. Lets change the story a bit, we needed a way of talking about $\infty$ and addition on the naturals for this whole setup to work for the problem at hand. Now addition is not a group operation on the set of natural numbers but we have a perfectly legitimate semigroup operation which extends addition to the set $\mathbb{N} \cup \{ \infty \}$. Just treat the added point as a zero under addition (i.e. $x + \infty = \infty + x = \infty$ $\forall x \in \mathbb{N} \cup \{ \infty \}$)
11. ## Find the value of x in this equation:

Ok, reread what you replied to again and i still can't see your connection.
12. ## solving this SDE

Why didn't you use Ito's formula?
13. ## Extremely difficult question from an IQ test...

Hi w=f[z] I got those solutions by just kicking out the equations for Marconi, Stern and Davison and solving the resulting system and then by kicking out the equations for Marconi, Stern and Cherenkov and solving the resulting linear system.
14. ## what's next?

Lol, this one is actually easy : just read the numbers out loud First Line : You have One One = Second Line Second Line : You have Two Ones = Third Line Third Line : You have One Two and One One = 4th Line 4th Line : You have One One and One Two and Two Ones = 5th Line 5th Line = You have Three Ones, Two Two's and One One so the next line is 312211
15. ## solving this SDE

Gogo, can you show me how you got that SDE from my suggested substitution?
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