Does anyone know the current method of (on the fly) inviting a user to a math chat? My rep is over 1000 and the user I wish to invite is at 21 rep. The old meta-math articles don't seem to work anymore.
Used to be named Ocean View but there were so many Ocean View's in California the mayor at the time renamed it Albany. I prefer Ocean View albeit Bay View would be more truthful.
Let's just make it kind of explicit what the row operation is. We have three elementary row operations: swapping rows, multiply rows by a non-zero scalar, and adding a multiple of one row to another.
well, Z/n is a product of F_qs as Z-modules, so End(Z_n) is a product of End(F_q)'s as rings and they have the same invertible elements, but why does this respect determinants
@BalarkaSen do you know Return of the Obra Dinn? A fellow PhD student suggested it to me and it looks great from the little I've seen (but I'm trying not to see much because I prefer playing games blind)
@AttractorNotStrangeAtAll Different folks have different approaches. My preference is to 'understand' the result first and often the proofs will follow from this 'understanding'. However you can spend many unproductive hours trying to reproduce results that took other years to develop without having a road map at least.
Sometimes I understand the theorems, I 'get' the concepts and definitions, I'm ok with the examples, but when I arrive at the exercises I feel like there's something there I don't really understand what's going on. So that's why I thought about changing my study strategy
"The Nielsen–Schreier theorem in turn implies a weaker version of the axiom of choice, for finite sets." Is Wiki trolling? Choice for finite sets is provable in ZF already or am I tripping?
@Thorgott not for all families of finite sets, not even for countable families of finite sets (that should be equivalent to what logicians call the weak Koenig's lemma)
ZF doesn't even prove choice for families of unordered pairs iirc
@copper.hat with everything remote is harder, and I'm doing classes as a non-degree student, so no one is really my friend
I'll try to record some videos of myself explaining some concept or whatever, because it makes me explain things out loud and clear my thought of what's happning, Idk
@AttractorNotStrangeAtAll I understand. I have only found one person in my career (I'm 60) who shares a similar perspective & interest in mathematics and with whom I would socialise independently of mathematical motivations.
Part of doing mathematics efficiently involves a directness that makes some uncomfortable.
Hi. Does anyone know where I could find a proof/explanation of this answer about how to Calculate 3D Vector out of two angles and vector length? https://math.stackexchange.com/questions/1385137/calculate-3d-vector-out-of-two-angles-and-vector-length
the description in that question is a bit strange, i think. it seems that $\alpha,\beta$ correspond to the angles of the vector upon projecting to the $XY$ and $YZ$ planes respectively
@copper.hat take the (X,Y,Z) point to be (1,0,0). then the projection into the YZ plane is (0,0)
whereas the conversion given in the answer would require $\alpha=\pi/2$ and $\beta=0$. that makes sense for spherical coordinates but not for the question itself
(unless, of course, the OP's description of their angles was so unclear that it was actually correct)
@jarlemag my reading of this is that, while that answer is fine for what it sets out to do, it doesn't really match the question as stated. but the lack of detail means i'm not really sure i understand what the OP asked for in the first place
I got a bit confused by the question (and a similar one here: stackoverflow.com/questions/30011741/…) too, but the basic question is still "how to get (unit) vector from two angles."...
I think this would be a statement applicable to my case: "α is an angle in the XY plane (angle from the X axis), β is an angle between the XY plane and the Z axis. Find the unit vector with direction defined by the angles.
I am given a formal grammar $G=(V_n,V_t,P,S)$ where $V_n$ is the set of non-terminals (variables), $V_t$ is the set of terminals (alphabet), both are finite, $P$ are the productions or grammar rules and $S$ is the start symbol
I am asked to prove or disprove $|L(G)|=|V_t^*|$, which is obviously false
I have shown that $|L(G)|\leq|V_t^*|$, where $L(G)$ and $V_t^*$ can be finite or infinite
Is this sufficient to show that $|L(G)|\not>|V_t^*|$ hence $|L(G)|\neq|V_t^*|$?
@Semimclassical: I tried to solve it this way before reading the questions/answers mentioned, but it doesn't seem to give right results. If anyone can see something obviously wrong, I'd be happy to learn where I misstepped:
α is an angle in the XY plane (angle from the X axis), β is an angle between the XY plane and the Z axis. Find the corresponding unit vector v.
We know that: x^2 + y^2 + z^2 = 1
Let f be the length of the projection of v into the XY plane. Then:
sqrt(f) = sqrt(x^2 + y^2)
Uh, I hope I remembered that trignometric identity right...
@Thorgott yeah but some symbols need to be put there, isn't it? I mean, the generated language can be equal to the set of all words of any length (this is what $V_t^*$ means), but not always. Of course it can occur that $|L(G)|<|V_t^*|$, but my question is: How can we explain that it is impossible -no matter what grammar is- that $|L(G)|>|V_t^*|$?
So my question, again, is: Is it sufficient to prove that $|L(G)|\leq|V_t^*|$ to conclude $|L(G)|\not>|V_t^*|$?
what I'm saying is that you should remind yourself of what those inequality symbols mean in plain language and then it will be very clear which parts of reasoning are sound and which aren't
Hello. I'm looking to ask a question concerning examples of finite concepts that require infinity. I'm not sure how it would be received. It might be too broad, say, or not phrased in a helpful way. Do you have any advice? What are your thoughts on some examples in the spirit of the question?
@Shaun I don't know much of this, but an example that comes to mind is the methods used in the study of finite simple group of Lie type. These can be described as $G(\Bbb F_q)$ where $G$ is an algebraic group. It turns out that it's often useful to work with $G(\overline{\Bbb F_q})$ when studying those, e.g. their representations
