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Forum: Puzzles 2017-06-03, 20:07
Replies: 10
Views: 945
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: 945
Posted By jinydu
Yup

Yup
Forum: Puzzles 2017-06-01, 19:47
Replies: 10
Views: 945
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: 63,923
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: 63,923
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: 63,923
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: 1,430
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...
Forum: Abstract Algebra & Algebraic Number Theory 2013-11-25, 09:01
Replies: 2
Views: 2,839
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.
Forum: Abstract Algebra & Algebraic Number Theory 2013-11-25, 04:48
Replies: 2
Views: 2,839
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...
Forum: Other Mathematical Topics 2013-05-25, 08:35
Replies: 11
Views: 2,203
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...
Forum: Other Mathematical Topics 2013-05-23, 07:11
Replies: 11
Views: 2,203
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)...
Forum: Other Mathematical Topics 2013-05-21, 22:25
Replies: 11
Views: 2,203
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...
Forum: Other Mathematical Topics 2013-05-21, 13:15
Replies: 11
Views: 2,203
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: 1,297
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: 1,297
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: 540
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: 8,837
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: 8,837
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: 8,837
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...
Forum: Abstract Algebra & Algebraic Number Theory 2013-01-02, 18:09
Replies: 5
Views: 3,942
Posted By jinydu
Oops. Yes, silly me, thanks.

Oops. Yes, silly me, thanks.
Forum: Abstract Algebra & Algebraic Number Theory 2013-01-02, 06:17
Replies: 5
Views: 3,942
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}'?
Forum: Abstract Algebra & Algebraic Number Theory 2012-12-31, 06:22
Replies: 5
Views: 3,942
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: 761
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: 761
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: 761
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?...
Showing results 1 to 25 of 1000

 
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