Hey I'm not bragging, guys. Who doesn't like a good grade? But would you be ok getting a salary without having done any work? Free money is nice, but after a while you would feel like something is wrong. I feel that something is amiss. It's like a trap to gets your hopes up with possibly false...
Hello. On fear of hijacking it, I didn't want to merge this with a similar thread earlier.
Have you ever received an undeserved GOOD grade? Such as an A+ in a class, when you feel you should have received a B, or B-?
I'm suspicious I'm getting better grades than I should. Yes, I am indeed...
Everything will come at the cost of the environment. I don't think eliminating those who oversee the protection of it---however muddled or inefficient these departments are---will help us survive as a species. I'd rather live in the dark and breathe clean air, than live in "modernity" and...
Sorry, I wrote the problem incorrectly. I meant to write:
fn converges uniformly to f, i.e. fn→f.
I don't know why I wrote "uniformly continuous" instead.....
I see what you mean though, adding and subtracting quantities. I'll start with that.
Homework Statement
I have a solution to the following problem. I feel it is somewhat questionable though
If fn converges uniformly to f, i.e. fn\rightarrowf as n\rightarrow∞ and
gn converges uniformly to g, i.e. gn\rightarrowf as n\rightarrow∞ ,
Prove that fngn...
Homework Statement
How do I determine the parity of a permutation? I think my reasoning may be faulty.
By a theorem, an n-cycle is the product of (n-1) transpositions. For example, a 5 cycle can be written as 4 transpositions.
Now say I have a permutation written in cycle notation: (1...
Ah, I was so convinced I could do something clever using just the ordering. Also, if you have the time to explain, why was the previous proof incorrect? I arrived at a contradiction. I see that I didn't make use of all the hypotheses; I'm wondering if that makes it an insufficient contradiction...
Sorry, I incorrectly typed this into Latex. I meant to say that the sequence n_i is a strictly increasing sequence. It is the sequence of all n for which n*x_n is greater or equal to epsilon. Progressing along the natural numbers, n(1) must be less than n(2), and n(i) < n(i+1). The contradiction...
I'm stuck on this one. I see how the proof fails, because epsilon/n isn't a constant, but now I'm not sure how x_n decreasing helps.
The most I can claim is that n*x_n is less than n*epsilon.
I see that n diverges to infinity, and x_n converges to zero, which gives a limit of...
This is an intro to analysis problem.
I have already finished this proof (see attachment). I would like someone to check it for me. Its really short and easy. Thanks! -Abraham
Tags:
-Cauchy series
-Infinite series
-Limits
This isn't really hw. I need someone to explain a certain line in a proof:
" b2 \leq \frac{1}{n} for all n in the natural numbers. This implies that b2 \leq 0 (a consequence of the Archimedean property). "
I don't see how the Archimedean is applied in this context. This is my understanding...
Hi Syrus. Do you mind clarifying? I don't think I understand what a traditional argument is. What makes a sound proof by contradiction? So far, I show, by contradiction that:
1.) x \neq 0 ---> x2+y2 \neq 0
2.) y \neq 0 ---> x2+y2 \neq 0
3.) x, y \neq 0 ---> x2+y2 \neq 0
Thus, x=0, and...
Is it a circle? The hw problem is for an intro to analysis class though, so I wonder if a geometric argument / proof would be accepted.
To dynamicsolo: Thanks, that's what I was looking for. I felt like I was missing something.
x,y are in R. Suppose x2+y2=0. Prove that x=0 and y=0.
My proof:
Suppose x\neq0, y\neq0. Then by the field axioms, both x2 and y2 are strictly positive, and so is their sum. This is a contradiction, since we supposed that their sum = 0.
Thus, x=0, and y=0.
This problem and proof...
I've taken a first semester course on PDEs. Basically all we learned was separation of variables and method of characteristics. I understand that there are transforms out there, such as laplace and fourier. However, it looks like there aren't many analytical ways of solving PDEs. Mind you, I'm...
For example, if I want to show that there is no real # solution to
x2 + 24x2 = -1
is it correct to show that
d2/dx2( x4 + 24x2 ) = d2/dx2(-1)
---> 12x2+48 = 0
And since x^2 is >0 or =0, 12x2+48 ---> 0 + 48 \neq 0
Therefore, there is no real number solution to x2 + 24x2 = -1...
Sorry about the botched thread title. I meant it to read "How many foreign languages can you take at once."
I'm wondering if there's a recommended limit for how much can be done at once? I'm not concerned with how much work it'll take, I'm concerned if there's a limit on my brain that I'm not...
Homework Statement
Find the general solution of
\frac{dy}{dt} = 2y +sin(2t)
Homework Equations
The general solution of a nonhomogeneous ode is the particular solution of the nonhomo plus the solution of the homogeneous ode.: y(t)= y_{p}(t)+y_{h}(t)
The Attempt at a Solution...
I'm actually tempted towards switching to nuclear engineering, or at least grad school in it. I think that the future of energy will depend on our ability to harness nuclear fusion.
You cannot produce something from nothing.
Energy cannot be extracted from nothing.
Of course we are all trying to find new sources of energy, help the environment, etc., but talking about impossibilities is not going to help.
I would like to submit my humble opinion, that maybe sciences are harder, because they're not human inventions.
The arts are human creations, about man, living, philosophies, and such experiences, etc. But sciences are about things that are abstract and truths that exist with or without...
Oh people will join groups on facebook, no doubt. But that'll be it exactly, and nothing more.
In my experience, the facebook people who join "groups" have lackluster will to produce meaningful action on behalf of that group.
For example, there was once a group protesting tuition hikes...
Yeah, its well within anyone's God-given capitalist right to charge whatever they want for their products. But just because you can charge exorbitant amounts, should you?
To do so, is obscene. At least that's my interpretation of the OP's mind.
Yeah, it costs a lot to apply to schools, and...
Yes, I would agree.
But, it remains that these costs are still substantial amounts to the student population, profit or non profit.
I think, instead (maybe this is too naive) that any college requiring SATs or SAT IIs, GREs, or any other ETS product should pay ETS a certain amount to fund...