"If $f$ is not continuous at $x_0$, then some $\epsilon$ cannot be matched by a $\delta$. In particular, the choice $\delta = \frac{1}{n}$ will not do. Why?
@MichaelAlbanese I don't know whether it goes through the review system, but it's visible in the "delete" tab of the pseudo-moderator tools page for users with high enough rep. I forget whether it's 10k or 20k.
@HenningMakholm I can see it so it must be 10k. If a question gets undeleted, do all the answers automatically get undeleted or do they have to be done manually?
@MichaelAlbanese Good question. I think answer is not actually "deleted" in itself but only shown as such by virtue of the question being in a deleted state. For example, there's no deletion event to see in the answer's history.
There was a time when mathematicians were kind When their functions were soft And their numbers inviting. There was a time when flags were blind And the mse had.jokes And the jokes were exciting. There was a time ... then it all went wrong
Hey guys. I needed help proving that if a group G has order 2n where n is a odd integer then G has only one element of order 2. Proof: We first show that there is at least one element with order 2. Suppose there are no elements of order 2. We also know |G| is even. Let a in G where a≠e then a,a^-1 must be distinct and occurs in pairs. But since |G|-{e}=odd # a contradiction. There exists a element of order 2. Suppose there exists a group G with two elements of order 2.
let a,b in G such that a^2=e and b^2=e. But if we remove {a^2,b^2,e} from G we are left with a odd number of elements => There exists a third element of order 2 a contradiction.
@user60887 you mean if we remove {a,b,e} you would have an odd number. the problem is you wouldn't be left with a group, so your previous lemma (odd order group implies elt of ord 2) does not apply.
Hey, I'm trying to show that sum from -infinity to + of cos(2 \pi n t) equals to the same sum of \delta(t-n) (n in N and Dirac's delta of course :) ), Any one has a hint?
could someone help me getting an idea why for commutative rings the following are equivalent: For every Ideal $\mathfrak{ab}\subset \mathfrak{p}$ implies that $\mathfrak{a}\subset \mathfrak{p}$ or $\mathfrak{b}\subset \mathfrak{p}$ and on the other hand $ab\in \mathfrak{p}$ implies that $a$ or $b$ are elements of $\mathfrak{p}$
@what'sup: what's important is the quality of your answers. There are some folks who post fewer, high-quality solutions. I look out for their input and hope to emulate that behavior.
@what'sup I am sure. Anyway, the challenge on this site is to find the wherewithall to post high-quality, easy-to-follow solutions that take on a life of there own, in the face of pressure to be the first to post.
what's important is the quality of your answers. There are some folks who post fewer, high-quality solutions. I look out for their input and hope to emulate that behavior.
@anon oh thanks the other direction is clear now, but do you really mean $ab\in \mathfrak{p} \implies a\in \mathfrak{p}\wedge b\in \mathfrak{p}$? This seems to be wrong, let $a$ be $0$ and $b$ be anything
How would you create a more challenging problem to this question (that uses the same concepts): Find the measure of an angle if 80 degrees less than 3 times its supplement is 70 degrees more than 3 times its complement.
@anon I don't see where we used that we are in a commutative ring, but we surely used it somewhere, because of in non commutative rings those things aren't equal
For example taking the $n\times n$ matrices, $\{0\}$ will surely fulfill property 1 but not the other
hi all, i'm trying to ask a question, but i have noticed that my equations come out ugly and hard-to-read. how do you create "beautiful" math formulas on this site?
Q: How do I type math in my question/answer/comment?
A: For simple formulae, you can use <sup></sup> to write superscripts and <sub></sub> for subscripts:
y<sub>1</sub>=x<sup>2</sup>+3becomes y1=x2+3
For more complicated formulae, you can use TeX markup.
To type inline TeX equations, surround...
@Ted It is humorous watching a quantum information theorist and a complexity theorist try and convince a group of black hole physicists by proving rigorous theorems
When we do tensor product of modules (at least finitely generated) it's analogous. With your poly question, we have to worry about double duality, and I actually don't know the answer.
@Ted I thought you might identify with that given your stated opinions (which i find myself more and more drawn to, particularly today as I saw the South Carolina quarterback who has earned the school millions (I'd bet) in ticket sales and alumni donations possibly blow out his knee ending his career without ever being paid 1 nickel.
Yikes ... And UGA is going down the tubes due to injuries, too, although presumably not life-ending. Glad you're adopting a sane — if anti-Southern — attitude.
Suppose $z_0=e^{i\theta_0}$ a complexe number as $\theta_0\in ]-\pi,\pi[ \setminus\{0\}$.
For $n\in \mathbb{N}$, we pose $z_{n+1}=\frac{|z_n|+z_n}{2}$ and $z_n=r_ne^{i\theta_n}$ with $(r_n,\theta_n)\in \mathbb{R}^+ \times ]-\pi,\pi]$.
The first question was determine $r_{n+1}$ and $\theta_{n+1}...
waking up is not a conscious action. deciding to get up is due to knowledge of the consequences of not doing so. only on some days do I actually want to get up - for example, if I have something cool to do that day.
debating whether to cram for a physics SAT test offered by collegeboard on november 6th, I have already taken the highest test they offer in mathematics
I don't really want to come off that 'well rounded', I wanted to just focus on my interest in mathematics, do you think it would be a bad idea to take the Math 1 test? Even if I could get a perfect score on it?
I have already taken there Math 2 test and got 800 on that, I don't think I could get 800 on the physics
Q: How do I type math in my question/answer/comment?
A: For simple formulae, you can use <sup></sup> to write superscripts and <sub></sub> for subscripts:
y<sub>1</sub>=x<sup>2</sup>+3becomes y1=x2+3
For more complicated formulae, you can use TeX markup.
To type inline TeX equations, surround...
Suppose $z_0=e^{i\theta_0}$ a complexe number as $\theta_0\in ]-\pi,\pi[ \setminus\{0\}$.
For $n\in \mathbb{N}$, we pose $z_{n+1}=\frac{|z_n|+z_n}{2}$ and $z_n=r_ne^{i\theta_n}$ with $(r_n,\theta_n)\in \mathbb{R}^+ \times ]-\pi,\pi]$.
The first question was determine $r_{n+1}$ and $\theta_{n+1}...
