Thank you for making this great material. You are easy to follow and to the point. Your comments about proof strategies, example vs non-examples, complex proof immediately followed by reminding us of the simple definition make these concepts easy to grasp. Beyond math, you have a great ability to teach. The M.I.T. students are lucky to have you as a professor. M.I.T., thank you for supporting open and free lectures.
There is a mistake in lecture notes, example 71. Example in the lecture notes picks epsilon_0=1/2 and then proceeds with 1=|(-1)^M-(-1)^(M+1)|. This is wrong. Epsilon should be 1; and the expression with absolute values evaluates to 2. The lecture video is correct, the lecture notes are not.
I was wondering the same thing but what matters is that by hypothesis |x_n - x | < 1 so the argument still holds because B then can only be even bigger
Thank you for making this great material. You are easy to follow and to the point. Your comments about proof strategies, example vs non-examples, complex proof immediately followed by reminding us of the simple definition make these concepts easy to grasp. Beyond math, you have a great ability to teach. The M.I.T. students are lucky to have you as a professor.
M.I.T., thank you for supporting open and free lectures.
The tracking camera is quite awful it makes the blackboard unreadable sad
Thank you for the series. Self-studying analysis (as many attempt) is difficult, but these videos offer a great supplement to reinforce ideas :)
is there a person behind the camera, the track is quite awful
heyyy stop moving the camera
It's a ai camera follows the prof
Thank you for making these videos!
a weird question but can we prove sequence xn is unbounded by introducing algorithm in it and then using Archimedean property
There is a mistake in lecture notes, example 71. Example in the lecture notes picks epsilon_0=1/2 and then proceeds with 1=|(-1)^M-(-1)^(M+1)|. This is wrong. Epsilon should be 1; and the expression with absolute values evaluates to 2. The lecture video is correct, the lecture notes are not.
Both work I believe. Of course, the absolute value does equate to 2 but >=1 is just a looser ineqn
how is a monotonic sequence like 1,1,1,1,1..... which is bounded convergent?
it converges to 1, you can verify this using hte definition of convergence
@@Nate3145-zt8rh bro you being disrespectful if you are that was good
how is x sub n -x =1
I was wondering the same thing but what matters is that by hypothesis |x_n - x | < 1 so the argument still holds because B then can only be even bigger
ah yes@@seancates8880
are you currently following this course?
and also 1+1-c is a mistake I think
"not the democratic national committee" =))))