@Matt: it would be great if you didn't add the (general-topology) to stuff like "is the one point in the one point metric space an open set"? I consider tags like (general-topology) or (ring-theory) or (number-theory) to be on a more advanced level than that what you learn in the first hour about a topic. For instance, I wouldn't add the ring theory tag to a question about expanding (x+y)^2 either.
Interested in it in general? I wanted enough to understand what I was reading. I actually went through a large portion on my brother's old abstract algebra text, which included a lot of group theory. It just didn't bear any mention about free products or such.
I've tried asking questions here (well, not in chat...) but I haven't understood most of the answers. This is actually the second book I checked out trying to figure it all out...
First book I got was on Diophantine equations. It had some info on the topic, but said it involved binary quadrativc forms which were not covered in the book.
I tried some of the problems anyway. One I got stuck on and asked about here. Someone recommended the text Binary Quadratic Forms by D.A. Buell, which I was fortunate enough to find from a local library.
I don't buy your comparison and I disagree that this question isn't general-topology. I don't see why the level matters. For example a question like "Is this structure a ring?" should be tagged ring theory because it's about rings. Be that as it may: I will refrain from retagging things with general-topology in the future. Mainly because I don't know where to draw the line but also because I assume that you know better than me so I don't want to disobey.
@KannappanSampath Just skimmed through quickly, but it looks like it covers only the case x^2-Dy^2=1. That I know how to do, if not all the theory behind it. But apparently, if it equals some other integer, there can be mutiple fundamental solutions. The link I provided does not cover how to find all the fundamental solutions.
@MattN Tags should also be useful for those interested in a topic for finding things. "Questions like why is $\mathbb{Z}/n\mathbb{Z}$ a ring?" is not of interest to someone who wants to see stuff about ring theory. Just because a ring is there doesn't make it ring theory. Same in this case: just because a metric space gives a topology (which you can't know if you ask that particular question) doesn't make it belong to the general topology tag in my opinion. The level definitely matters.
@KannappanSampath You claimed that we don't have an isomorphism $W \cong W^{\ast*}$. But if the map you defined is injective, by rank nullity wouldn't it be surjective too since $\dim W = \dim W^{\ast}$?
@Kannappan: this paper says that the non-existence of the projective plane of order 10 was proven by computer, much the same as the 4-color map theorem; checking a multitude of cases.
@robjohn Yes that is right. But, long before this proof appeared, it was shown that the automorphism group of the projective plane of order 10 is trivial.
Well, if you want to have three distinct letters, it means, you have one letter repeating twice and two letters different from each other and different from the repeating letter.
@tb I disagree with you very much. For example set-theory and elementary-set-theory is a case where it's been solved differently. But instead of having elementary-X we could introduce an elementary tag and then tag accordingly. In any case, I think you know what you're doing so I'm happy to conform with whatever you think is right.
@KannappanSampath Ok. Still need help with linear algebra? (Be warned though, I'm not sure I can help: ))
We had a user while ago, with a combinatorics problem. Robjohn and I solved it. Robjohn and I attempted to explain. The user just left without leaving a word!!! Crazy!
@KannappanSampath I haven't gotten a chance to read much of it. I was having trouble finding motivation for parts and so it was taking at while to push through on definitions alone. The definition of the incidence structure was a bit confusing; given $\{X,\mathbb{B},I\}$, is the $B$ used to define $I$ just an arbitrary subset of $2^X$?
@robjohn Yes, a kind of. Actually, I should admit, I made it look simple. The usual way of defining incidence, as done in most texts is rather confusing.
Me too, sometimes. I was trying to help someone with their homework and miserably failed. Maybe you can help me : ) The question is: How many 4 letter words can you make from letters in the word calcutta.
@HenningMakholm I have one slightly more specific question: a different thought I had was to first count all 4 letter words with all different letters. I have 5 different letters so I thought I get 5! different 4 letter words with all different letters. The problem is that that's already far more than 26. Is my counting wrong or do they mean actual words?
@MattN I agree on 5! -- each 4-letter string corresponds exactly to one permutation of the 5 letters (just tack the single unused letter onto the back).
basically counting valid sets of three dice where no matter which die you pick, i can pick one of the remaining two and beat you >50% of the time in terms of rolling a higher value
@Joe if you let u = x^2+4 then du is 2xdx. In your original integral, you then replace all your terms. x^2+4 turns to u and you replace 2xdx with du, leaving you with u^100 du
If I have three nontransitive dice with 6 sides each, with repeated faces allowed (even across all dice), and faces that can range in value anywhere from 1 to N, I am having difficulty figuring out a way to simplify counting valid sets for large N.
It doesn't seem to come down to things like exp...
Kind of a simple question, but what exactly are R-modules used for? Do they have any engineering applications?
