He said "overall" not for any spesific n u can pick, he explains that with the geometric example right after that minit mark. The point is; the supremum "overall" of those 2 sets, must be the greater one, not the spesific intervals u can pick that are inside the bigger one. At least thats what im getting, or u are right well... i guez i dono unless elliot himself comes and clarify this.
Thank you very much for your playlist! Thwere is only thing to fix - at 19:40 I think that -- sup_n{|x_n| + |y_n|} \le sup_n{|x_n|} + sup_k{|y_k|} For example consider finite sequences: x=[0,1,0] y=[0,0,1]
Ok, everything sounds perfect except the usage of Natural Numbers. Do we have to assume that both sequences {x_n} and { y_n} have the same number of sequences. Is there an order in the sequence {x_1, x_2 ,x_3..... x_n} that x_1
your videos boost up me when I loose my confident .thank you sir.
Im going to work hard on this playlist as a whole! Thnak you!
you are saviour!! Thanks a lot for uploading these videos
Thank for the video. Nice explanation.
@18:02 you mentioned sup(|x|+|y|) = sup(|x|) + sup(|y|)
That is not necessarily true. Take the following example:
x = {1,2,3,1,2,3,...} => sup(|x|) = 3
y = {3,2,1,3,2,1,...} => sup(|y|) = 3
x+y = {4,4,4...} => sup(|x| + |y|) = 4 < sup(x) + sup(y) = 3 + 3 = 6
In this video what is the meaning of Mx and My. Could you please give some examples?
I think he meant to put sup(|x|+|y|)
Alternative proof:
For every n
|xn-yn|
He said "overall" not for any spesific n u can pick, he explains that with the geometric example right after that minit mark.
The point is; the supremum "overall" of those 2 sets, must be the greater one, not the spesific intervals u can pick that are inside the bigger one.
At least thats what im getting, or u are right well... i guez i dono unless elliot himself comes and clarify this.
Thank you very much for your playlist!
Thwere is only thing to fix - at 19:40 I think that -- sup_n{|x_n| + |y_n|} \le sup_n{|x_n|} + sup_k{|y_k|}
For example consider finite sequences: x=[0,1,0] y=[0,0,1]
you are right
trueeee, from his real analysis course
I would like to get in touch with you if possible. I need a serious help in Functional analysis.
Ok, everything sounds perfect except the usage of Natural Numbers. Do we have to assume that both sequences {x_n} and { y_n} have the same number of sequences. Is there an order in the sequence {x_1, x_2 ,x_3..... x_n} that x_1
no habla solo de sucesiones monotonas, habla de suceciones en general, de "todas las sucesiones ACOTADAS".
For all N. For all n. OMG ahahahhaa..
But these videos are great!
Thanks..
Nice 👍🏽
I got lost due to the Scribbles ☹️
∞