Real Analysis Ep 9: Limit rules

Episode 9 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class.

This episode is about limits of sequences.

[mgmartin]

Duffer here. I think I’m really beginning to understand. (Cue ape taking up thigh bone and smashing pile of bones…). Monolith stands by.

[mbmathworks]

The correlation coefficient of your gift in teaching math plotted against Bob Ross' gift of teaching painting is exactly 1.

[quant-prep]

damn this guy is definitely a god sent!

[isharauditha]

this content was very helpful to me.thank you so much

[badchessplyr]

this may seems trivial but i don't get it . At 4:00, if (n^2 )/(n^3+2) < ε and (n^2 )/(n^3+2) < (n^2)/n^3, then how did you conclude (n^2)/n^3 < ε, if a<b and a < c, how does it imply b <c, for example 5<6 and 5 <8 but 8 <6 is not true.

[john-oiuz]

sorry i want to ask for the question at 12:30, why we not write N>1/2s in stead of N = 1/2s
and can i also view the homework exercise to practice please?

[pulkitmohta]

At 29:35 instead of taking ε/2 for both sequences, can we take, say, ε/4 and 3ε/4? Isn't it not necessarily true that both sequences would start converging for same ε/2?

[sanjeev]

At the frame 7:00, where you are about to rub the board, shouldn't N be (N > 1/epsilon) instead of (N = 1/epsilon)?

[hunterroy]

Is math more about counting or is math more about logic and craftiness?

[ashraygupta]

After learning this epsilon method, I was looking at the question 'Let (xn) be a real sequence such that xn→x(x not equal to 0) Then there exists N such that for all k≥N we have |xk| ≥ |x|/2' and trying to do it using this method because the language almost looked familiar to the approach we used in the video, but I hit dead end after dead end, could this be done using the (epsilon and N) method?

[igorfritz]

what intuitively is epsilon greater than 0 mean