Lecture 7: Convergent Sequences of Real Numbers

[@gregmcmahan7420]

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.

[@evionlast]

The tracking camera is quite awful it makes the blackboard unreadable sad

[@scottsobolewski1041]

Thank you for the series. Self-studying analysis (as many attempt) is difficult, but these videos offer a great supplement to reinforce ideas :)

[@assalamihoub1806]

heyyy stop moving the camera

[@tommyshelby6277]

It's a ai camera follows the prof

[@Maria-yx4se]

is there a person behind the camera, the track is quite awful

[@mattetor6726]

Thank you for making these videos!

[@MrScattterbrain]

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.

[@tyx7650]

Both work I believe. Of course, the absolute value does equate to 2 but >=1 is just a looser ineqn

[@rashpalsingh7421]

a weird question but can we prove sequence xn is unbounded by introducing algorithm in it and then using Archimedean property

[@rashpalsingh7421]

how is a monotonic sequence like 1,1,1,1,1..... which is bounded convergent?

[@acetonewong4608]

it converges to 1, you can verify this using hte definition of convergence

[@rashpalsingh7421]

@@Nate3145-zt8rh bro you being disrespectful if you are that was good

[@rashpalsingh7421]

how is x sub n -x =1

[@seancates8880]

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

[@rashpalsingh7421]

ah yes@@seancates8880

[@rashpalsingh7421]

are you currently following this course?

[@rashpalsingh7421]

and also 1+1-c is a mistake I think

[@021scorpion]

"not the democratic national committee" =))))