Introduction to Sequence Spaces Part 1

[@asemabdelraouf7161]

At 15:56 an < bn implies that lim an

[@mmackeviciu125126127]

I guess in the specific example he gave, if bn is the sequence on the right then the inequality is indeed strict, since |xn-yn|/(1+|xn-yn| < 1 always, hence every term in the sequence on the left will be strictly smaller than every term on the right. He should have been more precise.

[@colinmundy9836]

Why us an+1 - an strictly greater than zero? Could the n+1 term in the x sequence and y sequence not be equal to each other and thus give us a modulus of zero?

[@duckymomo7935]

I don't think you should use i in the metric defitinion because it confused me between index and imaginary number

[@dionsilverman4195]

Exactly

[@claudiagaudino2469]

I swear to god I was like: "ooook I guess we have an esponential complex function to start with"

[@tekaaable]

Thank you!

[@zl7460]

although conclusion is true, your contradiction proof was wrong

[@debendragurung3033]

2:30 what exactly is that formula called?

[@julians3084]

Have you found out what it is called?

[@semaisamir2050]

Epsilon should be kept the same for the contradiction, and just reverse "there exist" in front of N by "for all", instead of "not exist", and at the end, reverse the inequality |an - supT| should be greater or equal than epsilon

[@jobel6589]

it is just the same.

[@RealMcDudu]

You are so rigorous sometimes I just have to skip forward :-P But good videos non the less.