Ok.. I have to know.. are you writing backwards.. or is this a mirror. It’s distracting me trying to figure out the exactly what is going on with how/what you’re using to write on. Sorry, I know this is silly. But really... it’s playing mind tricks on me. Please tell me so I can stop wondering and pay more attention to the math. HA!
The plane is open since any point in the plane can be surrounded by an open neighborhood (set). We say a set is closed if its complement is open. (complement meaning everything that's not in the set) Since the complement of the entire plane is nothing - the empty set -(which is open by definition), the plane is closed. Alternatively, you could think of the plane containing its (trivial) boundary - as it is unbounded. I hope that wasn't too wordy and that it helped you out!
Check out the previous episode!
th-cam.com/video/_HRu0gfgcFE/w-d-xo.html
BriTheMathGuy I'm going to be taking my first course in analysis in the fall. What are your opinions on Baby Rudin?
I am not familiar with their work, but books reviews on amazon seem to be fairly positive. Best of luck with your course!
@@BriTheMathGuy Where can I find the answer to why the complex plane is both open and close? how's it possible to be both at the same time?
your playlist is a life saver. your explanations are so clear and concise
Thank you so much! Your series really helped clear so many doubts
Very glad it could help!
Thank you so much!!!! U helped me a lot!
Glad I could help!
Thank you very much! ❤️
You're very welcome!
great man thanks for you help
Thanks a lot Sir!!!!!!!!!!!!!
Most welcome!
Thank you so much bro. All the way from Tanzania(East Africa)
super helpful. Thank you
Nice one
Is it because the complex plane trivially includes all of its zero boundry points.
Yes! Nice job, the complex plane is unbounded. (No boundary points)
The comlex plane has no boundary points. Therefore it is Open because a closed set will have to contain its boundary points
Shukriya,,
Ok.. I have to know.. are you writing backwards.. or is this a mirror. It’s distracting me trying to figure out the exactly what is going on with how/what you’re using to write on. Sorry, I know this is silly. But really... it’s playing mind tricks on me. Please tell me so I can stop wondering and pay more attention to the math. HA!
This is due to the magic of video editing :)
what is meant by trivial?
not interesting like y'+y=0 y=0 is a trivial solution
Why is the complex plane both open and closed?
The plane is open since any point in the plane can be surrounded by an open neighborhood (set). We say a set is closed if its complement is open. (complement meaning everything that's not in the set) Since the complement of the entire plane is nothing - the empty set -(which is open by definition), the plane is closed. Alternatively, you could think of the plane containing its (trivial) boundary - as it is unbounded. I hope that wasn't too wordy and that it helped you out!
why ?
Why not :)
I was looking for these terms on TH-cam and found this one... 🥹🥹🥹 I'm glad that I found you Sir.. thank you so much. This was very helpful.