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 Showing results 1 to 25 of 1000 Search took 0.18 seconds. Search: Posts Made By: jinydu
 Forum: Puzzles 2017-06-03, 20:07 Replies: 10 Views: 1,400 Posted By jinydu 1) Well \mathbb{Q} (the set of rationals) has... 1) Well \mathbb{Q} (the set of rationals) has height \aleph_1, despite being countable. One can show by transfinite induction that every countable \alpha embeds into \mathbb{Q}, and taking the \sup...
 Forum: Puzzles 2017-06-02, 19:41 Replies: 10 Views: 1,400 Posted By jinydu Yup Yup
 Forum: Puzzles 2017-06-01, 19:47 Replies: 10 Views: 1,400 Posted By jinydu Heights of Models of PA This question is inspired by an incomplete solution of mine to a final exam problem a few years back. For M a countable model of PA, let \text{height}(M)=\sup\{\alpha:\exists f:\alpha\rightarrow...
 Forum: News 2016-02-01, 09:41 Replies: 631 Views: 75,320 Posted By jinydu Any update on whether there are going to be new... Any update on whether there are going to be new pins for M49?
 Forum: News 2016-01-23, 18:43 Replies: 631 Views: 75,320 Posted By jinydu Well I can't find it at all by browsing the... Well I can't find it at all by browsing the relevant subforum. I mean, the last post is 29 Mar 2013, but I can't find a thread whose last post is that just by browsing. Was only able to find it...
 Forum: News 2016-01-23, 18:21 Replies: 631 Views: 75,320 Posted By jinydu Haven't been keeping up much in recent years, but... Haven't been keeping up much in recent years, but just saw a Facebook post today. Looks like I've got not just 1, but 2 new prime discoveries to catch up on. The forum thread with the previous...
 Forum: Homework Help 2015-03-20, 17:51 Replies: 2 Views: 1,825 Posted By jinydu Conceptual Question about Implicit Partial Differentiation I think I should already know this, but... Problem: Given an equation of the form f(x,y,z) = 0, find dz/dx. Procedure: Take the partial derivative of both sides wrt x, using the Chain Rule and...
 2013-11-25, 09:01 Replies: 2 Views: 4,734 Posted By jinydu Never mind, found an example: The ring of... Never mind, found an example: The ring of polynomials (in one variable) with natural number coefficients.
 2013-11-25, 04:48 Replies: 2 Views: 4,734 Posted By jinydu Discrete Ordered Rings? Are there any examples other than \mathbb{Z}? (Alright, alright. I know of one other example: \prod_U\mathbb{Z}, i.e. ultrapowers of [tex]\mathbb{Z}[tex]. But this is not helpful for the problem...
 2013-05-25, 08:35 Replies: 11 Views: 3,070 Posted By jinydu The professor said this was an "easy" result...... The professor said this was an "easy" result... Guess I should feel good about not being the only one who doesn't see it right away...
 2013-05-23, 07:11 Replies: 11 Views: 3,070 Posted By jinydu How about a concrete example? Take M to be the... How about a concrete example? Take M to be the closed unit disc in the complex plane. Then its boundary is the unit circle. Taking U = {re^it: r>1/2}, we get a diffeomorphism of U with S^1 x [0,1)...
 2013-05-21, 22:25 Replies: 11 Views: 3,070 Posted By jinydu Here's the partition of unity theorem: Let X... Here's the partition of unity theorem: Let X be a manifold. For any covering of X by open sets {U_alpha}, there is a sequence of smooth functions {theta_i} on X such that: (a) 0 <= theta_i <= 1...
 2013-05-21, 13:15 Replies: 11 Views: 3,070 Posted By jinydu Manifolds Question Let M be a compact n-manifold with boundary. Show that there is an open set U containing the boundary that is diffeomorphic to (the boundary) x [0,1) -------- By definition of the boundary of a...
 Forum: Puzzles 2013-03-20, 12:57 Replies: 4 Views: 1,421 Posted By jinydu Thanks for the links. I already read Journey... Thanks for the links. I already read Journey through Genius in high school; that's where I learned of this solution! Going to have to think about the Weierstrass Factorization and it's application...
 Forum: Puzzles 2013-03-20, 01:05 Replies: 4 Views: 1,421 Posted By jinydu Can Euler's Basel Solution be Saved? I'm thinking of giving a talk to an undergrad math club, and I had the idea of presenting Euler's solution to the Bessel Problem (1 + 1/4 + 1/9 + ... = pi^2/6) as the topic. While there are some very...
 Forum: Lounge 2013-02-20, 07:14 Replies: 5 Views: 759 Posted By jinydu Higgs Boson and End of Universe? This sounds interesting... http://www.livescience.com/27218-higgs-boson-universe-future.html But, I don't really trust popular science article to get something like this right. For some reason,...
 Forum: Lounge 2013-02-15, 22:06 Replies: 205 Views: 10,121 Posted By jinydu (Could have been worse. You could have said God... (Could have been worse. You could have said God of War III. Besides, I think I could have handled that fight more intelligently.) Wish granted. Intel's and Microsoft's CEOs show up to the next DC...
 Forum: Lounge 2013-02-15, 21:43 Replies: 205 Views: 10,121 Posted By jinydu Wish granted. Unfortunately, out of frustration... Wish granted. Unfortunately, out of frustration at being unable to find a prime, Uncwilly sabotages his farm, leaving you just a twisted heap of broken plastic and metal. I wish to be Zeus...
 Forum: Lounge 2013-02-15, 05:04 Replies: 205 Views: 10,121 Posted By jinydu Wish granted. In order to ensure that ethanol... Wish granted. In order to ensure that ethanol preparations have no effect at all after the 2-3 hour buzz, including social effects and property damage caused by acting foolishly, you lock yourself...
 2013-01-02, 18:09 Replies: 5 Views: 6,364 Posted By jinydu Oops. Yes, silly me, thanks. Oops. Yes, silly me, thanks.
 2013-01-02, 06:17 Replies: 5 Views: 6,364 Posted By jinydu Thanks. I presume 'rational integer' and... Thanks. I presume 'rational integer' and 'rational prime' mean 'element of \mathbb{Q}' and 'prime in \mathbb{Q}' respectively? As opposed to 'element of \mathbb{O_K}' and 'prime in \mathbb{O_K}'?
 2012-12-31, 06:22 Replies: 5 Views: 6,364 Posted By jinydu Factorization of Ideals in Number Field, Looking for Reference Let K be the number field \mathbb{Q}(2^{1/3}). Find the factorizations of (7), (29) and (31) in O_K. I know there's a theorem by Kronecker that says (7) is reducible iff x^3\equiv 2 \text{mod }7,...
 Forum: Lounge 2012-07-12, 09:47 Replies: 14 Views: 1,070 Posted By jinydu Just checking in to this thread again... ... Just checking in to this thread again... Perhaps I should have been even more explicit. I'm looking for the name of a specific test that allows one to accept or reject the null hypothesis, which...
 Forum: Lounge 2012-07-06, 11:00 Replies: 14 Views: 1,070 Posted By jinydu Well, that was fun, and a bit tiring. I didn't... Well, that was fun, and a bit tiring. I didn't know about the 10,000 character per post limit, which prevented me from asking my question in the original post. Anyway, my question was this: Is there...
 Forum: Lounge 2012-07-06, 10:47 Replies: 14 Views: 1,070 Posted By jinydu Statics Question, in the form of a storey --- Part 1 --- Alice: Hello Bob. So glad you could spare a few minutes out of your busy day. Bob: No problem Alice. It's on my way back home anyway. Now what did you ask me to come for again?...
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