Recent content by Whovian

Ah, derp. There was something obvious. It turns out M is to be interpreted as the codomain of the free module homomorphism corresponding to A.

This isn't a homework problem, but rather a bit of confusion regarding something in the textbook we're using; if this isn't the right place, feel free to move it. From Artin's Algebra pages 422/423 (slightly paraphrased): Let ##Q=\begin{bmatrix}1&\\3&1\end{bmatrix}##...

You might want to take a look at GeoGebra; I seem to remember it can do that sort of stuff. Mostly geometry diagramming, but it can do graphing.

The problem here is that ##\binom{n+1}k=\binom nk+\binom n{k-1}## only for k>0; if k=0 then it's just ##\binom nk##, as both are 1. I think the convention is often to let ##\binom n{-1}=0##; then ##\binom{n+1}k=\binom nk+\binom n{k-1}## even when k=0.

It should be a cylinder-like thing with a vertical-convex bit which would correspond to the vertical bit of the cylinder, minus two filled cones. This is far from a rigorous treatment of the problem, but my reasoning goes something along the lines of this: Orient everything so the cone is...

So, while solving a problem a friend came up with involving the Totient function, I ended up doing a bit of research into the average asymptotics of the function. On page 268 of Introduction to the Theory of Numbers, it's mentioned that "The average of order of ##\phi\left(n\right)## is...

Firstly, if this is an inappropriate forum for this thread, feel free to move it. This is a calculus-y equation related to differential equations, but I don't believe it's strictly a differential equation. The question I'm asking is which functions...

Ah. "A power of an odd prime, twice the power of an odd prime, and for 2 and 4." *Collides hand with forehead to indicate frustration with self*

Would the Vietoris Topology over R2, along with the net definition of convergence, give the "correct" limit of these sequences of polygons? And would the limit of the lengths of a sequence of curves be the length of the limiting curve?

Sounds a lot like elements of a real projective space (take the n-dimensional vectors, 0 excluded, and call two of them "equal" if they're scalar multiples of each other.) For instance, a vector v is "equal" to -v since v=-1*-v. Not quite, though, since two vectors are still considered...

In an attempt to prove a statement about the residues of a certain sequence mod ##10^n##, I've derived something which seems to be in direct violation of Carmichael's theorem. Of course, this can't be right, so can someone either explain what bit of my reasoning is wrong or why this isn't in...

I'm used to normal being defined as "closed under conjugation by elements of G." Is there a different or equivalent definition I'm missing or something else obvious which makes clear that only one 7-subgroup existing means said subgroup is normal? (Knowing me, most likely.)

There must be a 7-subgroup; I just don't see why it must be a normal subgroup.

Homework Statement While reading through my textbook on abstract algebra while studying for a test, I ran across the following statement: There are two isomorphism classes of groups of order 21: the class of ##C_{21}##, and the class of a group ##G## generated by two elements ##x## and...

So, basically, a quasi-ordinal knowledge space is a slightly weaker structure than a topology (only closed under binary and therefore by induction finite union instead of arbitrary union?)