Recent content by Polamaluisraw

By definition of an open set we can show [0,1] is not open. since 1 is contained in [0,1] then for [0,1] to be open there must exist an ε>0 such that Bε(1) is contained in [0,1] for any ε>0. it is clear that Bε(1) is not contained in [0,1] because for any ε>0 1+ε is not contained in the set...

yes, either of the end point since they are included in the set. if you were to place an n-ball centered at either of those points it would leave the set?

First off thank you for the replies. I found this and wanted to show you all to see if this might be the problem.. http://science.kennesaw.edu/~plaval/math4381/openclosed.pdf at the bottom it has "techniques to remember" the way they are listed I though it was sufficient enough to...

we haven't gotten to basis elements, we JUST started talking about a topology. Could I assume that [0,1] is open and then show that because ℝ\[0,1] is not closed (it is a union of open sets) then it must be true that [0,1] is not open in the first place.

Homework Statement Show [0,1] is not open in ℝ Homework Equations [0,1] is open if and only if ℝ\[0,1] is closed. The Attempt at a Solution ℝ\[0,1] = (-∞,0) U (1,∞), this set is open. Despite the if and only if statement this is enough to say that [0,1] is not open in ℝ. Is this correct?

thank you for the response. I really hope that steady improvement will show that I am a capable student. My major GPA is great, do you think that will be able to offset my poor performance in my early years/non-major classes?

thank you for your response!

I want to get into a math program. I'm really interested in algebra, I do not have any clue as to what I would like to research, but I have not had that much exposure to it yet. But I know I would like to move in that direction. I'm really just curious as to my chances at acceptance into a...

Hello, I am two semesters away from my BS in Math and I very much want to pursue a PhD in mathematics. I started off very rough in college and it has taken me all the way until now to get my GPA up to 2.8 (terrible I know). My first two years were awful. last year I really turned things...

so instead of isin(t) just simply sin(t) ∫_{\gamma}(x-y)dz = ∫_{\gamma}(cos(t)-sin(t))dz ∫cos(t)dz-∫sin(t)dz every time I try evaluating the above expression I never can seem to get the correct answer. I'm using ie^(it) for my dz AHHH I am getting so frustrated. I feel like I am missing an...

Okay this is what I have so far: ∫_{\gamma}(x-y)dz where \gamma has parametrization: z(t)=e^{it} for \pi/2\leqt\leq3\pi/2∫_{\gamma}(x-y)dz = ∫_{\gamma}(cos(t)-isin(t))dz which we can break up like, ∫_{\gamma}(cos(t))dz - i∫_{\gamma}(sin(t))dz since z(t)=e^{it} then dz=ie^{it} so we have...

I don't understand how to set up a substitution so I can get it into a form that I know how to work with

could you elaborate just a little more? I really appreciate your help

Homework Statement ∫_{\gamma}(x-y)dz where \gamma has parametrization: z(t) = e^{it} for \pi/2 \leq t \leq 3\pi/2 Homework Equations the integral of the sum is the sum of the integralThe Attempt at a Solution I tried to break it up and see if I could evaluate it as I normally would but it...

Homework Statement I do not have specific problem, I am struggling in my complex variables class and I think a large part of it is because I struggle at sketching regions in ℂ. For instance let z=x+ I full understand what |z|< 1 looks like and all that (punctured disk, things in that...