One of the exams I graded yesterday belongs to a girl that retakes the course. She failed then and she failed now. I tried to see if there were four more points to give her somehow so she can pass... alas there were none in the question I graded.
@KannappanSampath If you feel so strongly about it, then it would be the way to go. But note that he did explicitly say that he didn't downvote your answer and I see no reason not to believe him -- but then I don't get his $-1$... Be that as it may, you'd better talk to the moderators about this.
@MattN I also spend quite a lot of time trying to figure out what they write and whether or not minor mistakes are due to confusion or not.
I'm grading a question about Cantor's theorem+Proving the statement that if $|A|=|B|$ then the collection of finite subsets of $A$ is equinumerous to that collection of $B$.
Quite the simple question really, but people insist on claiming "For every set $A$, we know that $|A|=|Fin(A)|$..." which is a bold contradiction to the first part of the question: Cantor's theorem!
I mean, so a connected subset of $\mathbb Q$ is also connected in $\mathbb R$. The intervals that contain only rational numbers are degenerate. Is this fine @Asaf?
In the infinite case we only teach the countable case too, since the course makes no use of the axiom of choice... so there's no good reason why it holds for "every infinite set".
@KannappanSampath That's better. Although slightly hard to understand that you mean to hint that $\mathbb Q$ is totally disconnected.
Can someone suggest me a linear algebra text? I am overwhelmed by the intriguing connections in the subject. I would like to understand them more clearly. I have read Artin and Herstein. So some other suggestions will help.
@Ilya Did you figure out the question that you posted and deleted shortly afterwards? Note that you can decompose your space into two pieces $B$ and $B^c$. On $B$ you look at the subspace $\sigma$-algebra (or its completion) and on $B^c$ at the $\sigma$-algebra of sets that are either null or equal to $B^c$ up to a null set. Now observe that the disjoint union of measure spaces is again a measure space and it coincides with the space you're interested in.
@tb: thanks - it was the first experience for me to deal with this stuff. I decided to prove it by showing that if we take the intersection of the generated sigma-algebra with the collection of sets satisfying the desired property, it will still be a sigma-algebra containing the same basis. Somehow it is similar to the proof you've mentioned
Would it be exaggerated to add a sentence to the graph theory tag wiki saying something of the form: "this is not for functions and their graphs, use (functions) instead"
@MattN Prancing around bare-feet in the meadows, picking flowers in order to make daisy chains? Why not. Sounds like a plan! I'm going to go as soon as I can...
@Ilya Well I interpret this one to be in the same category as the question about my hairstyle the other day... except for there I assumed it wasn't intended. : )
@tb: just fixed it: missing $$. I would like to ask you just to read the proof of the claim - that is essentially the fact we were talking about this morning
@MattN basically, yes. Two problems: 1. in your formula only the one involving $g$ (or $g_m$ for that matter) makes sense 2. the $g_m$'s aren't compactly supported, so some modification of the argument for $C_{c}^\infty$ must be made. Nothing very serious, though...
@MattN very good for the first thing. One of the worst songs? Well, I could show you far worse, but it's okay, it's not one of my beloved ones either. It's just the only one I could remember that featured people dancing around hippie-style for sure...
@MatsGranvik it's a really nice picture. I don't know the Mahonian numbers either, but it looks fascinating, this combination of noise and the Sierpinski triangle. Thanks for the link!
"Yes. I'm also simple minded: I enjoy reading "trash"."...."@MattN what's wrong with trash? It can be very enjoyable..."............I get this interpretation that simple minded people do not read anything that is enjoyable........Am I right @tb ?
Sachin : "Doesn't matter how many hundreds you score, you still have to put your head down and grrind it out for the team", "Enjoy the game and chase your dreams"
How unpredictable: the girl's fallen for him and after saving his life she's thrown away all of his clothes and now that the doctor has left they're all alone in a hotel room... I wonder what is going to happen next.
@MattN I was reading Borges this morning - I do like when from the first novel I understand that the writer is just awesome: in the plot, in the language, in his philosophy
@Dan : I don't mean anything wrong....I am just wondering that in India ...forget about internet/laptop....students are not even allowed to turn their head in a classroom
