Recent content by alexcc11

We haven't been given the definition. One of the other problems left in this problem set is to come up with a definition of a closure interms of a line R where R is all real numbers

I'm going to head off to sleep now since it's 1am here, but thank you so much for your help. I get back to you tomorrow. Thanks again so much

I get that it's not closed since the set is open, with < as opposed to <=, but I don't understand how a set that is open, can still have a closure. I have a hard time picturing that. I do agree with the rest however. I suppose the boundary would be the set it's self, -pi<arg(z)<pi or would that...

The closure of E is the the boundary of the closed set along with the inner regions, I thought. We haven't fully defined a closure in class, which is why I was unsure as to why this is classified as a closed set if it goes on forever everywhere when arg(z) doesn't equal pi+2kpi.

Yes. I get that. But I'm lost as to how use that with the problem?

You would end up on the opposite side rotated 180 degrees...

pi/2 brings the angle to the imaginary axis and another pi/2 you're asking? It would bring it back down to the real axis at +pi. I don't understand what you're saying about the arg of those numbers. Isn't it just 0 to pi/2 to get to the imaginary axis and another pi/2 to get back down to the...

From the real axis to the imaginary axis it would be from 0 to 0+90i or 0+pi/2 i? and from the imaginary axis back down to the real axis would it be pi or 180 + 0i?

From the real axis to pi wouldn't it just be 0+ik to 180+ik where k is any real number?

We haven't really covered what arg(z) is equivalent too. I know it's the angle, but we never went over how to find the z value within arg(z). I looked it up and it says it's equivalent to atan (imag(z)/real(z)), but I've never heard of atan, so I'm lost there too. Can't you specify the closure...

arg(z) is the angle from the real axis to z. So arg(z) inplace of z in the closure? I just started this class this week, so sorry about that.

Cl(E)={zεC : z=Cε∏+2k∏, k ε Z} The closure is equivalent to the entire plane excluding z=pi+2k*pi where k is in integer.

I see what you're saying. It would be all real numbers excluding any number differing from pi by 2pi*k right?

Why would it need to differ from pi by a multiple of 2pi? 2π+π=3π or π and 2π-π=π as well. They are the same thing

180 is equivalent to pi. Wouldn't it only not be able to be: z≠0+2k*pi? Why can't it equal pi?