That was absolutely incredible. What a beautiful and eloquent way to break down that proof. I am one semester away from graduating with my BS in applied mathematics, and I wish I had stumbled upon this video much sooner. The breakdown of this proof is the closest thing I’ve encountered to some sort of algorithmic method. Truly amazing!
Wow i just found your channel and im so grateful that you have tons of analysis and algebra vids ... im taking these classes next year and this will be a big help!
Or are we just saying use Archimedes to round up to the next highest whole number? Because that might explain why is would be strictly greater than but not equal to.
Why isn't the method used by calculus in the first column enough to prove your claim that the limit of the sequence as it goes to infinity is 2? Is it really necessary to develop all the rest (columns 2 and 3) in order to prove that the limit you found by applying l'hôpital's rule or whatever other calculus method previously used is actually the limit of the sequence? I don't really think so! Am I wrong? We do it just for the fun of using Cauchy's definition of limit? What's the thing after all?
great video! could you maybe do another in which the numerator does not simplify to a whole number as these are the kinds of questions I have on my exams, Thanks
14:30 if (2/epsilon) - 1 is an int though, wouldnt it be an equality and not satisfy the inequality ? F.E. epsilon = 2 -> N = 0 -> abs( 2/0+1) !< epsilon So either its all "N"
So I can literally understand all of RU-vid videos on my university subjects but I can't understand my lecturers ! I feel sorry for the money I pay ... Why can't they just put it like that!!
Your video is ok and good but you talk too much over very simple issues in the calculation. It nugs and one gets tired of the video due to too much talking, otherwise, great work. Thanks alot.
