# Recent content by Abraham

1. ### What to do with undeserved GOOD grades?

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...
2. ### What to do with undeserved GOOD grades?

I'm afraid people might be lying to me with the grades they give, that's all.
3. ### What to do with undeserved GOOD grades?

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...
4. ### YOU!: Fix the US Energy Crisis

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...
5. ### Trying to Prove Uniform Convergence: Analysis II

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.
6. ### Trying to Prove Uniform Convergence: Analysis II

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...
7. ### Abstract Algebra: Parity of a Permutation

Thank you, for the swift reply.
8. ### Abstract Algebra: Parity of a Permutation

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...
9. ### Intro Analysis: Proof that a limit = 0

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...
10. ### Intro Analysis: Proof that a limit = 0

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...
11. ### Intro Analysis: Proof that a limit = 0

So I went about thinking, and here's my new proof. Thanks for the help!
12. ### Intro Analysis: Proof that a limit = 0

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...
13. ### Intro Analysis: Proof that a limit = 0

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
14. ### Help Me Understand the Archimedean Property

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...
15. ### Please check my (simple) proof. Skeptical of its simplicity

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...