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.
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"
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
So I can literally understand all of UA-cam 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.
Nobody can explain that better. Good job. I wish our university had a lecturer like you.
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!
THIS IS THE BEST DETAILED AND SIMPLIFIED EXPLANATION I saw.
Excellent video, super clear. Thank you Matthew!!
You made things so much simpler. My professor is just as good at teaching but needed a refresher!
That was the BEST explanation I've seen so far about this topic. Thank you so much!!
Thank you Matthew. This is very helpful to me in my Advanced Calc course. Much appreciated!
thank you for explaining this in the best way possible. you make maths seem like a piece of cake
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!
honestly the best explanation i've found
You seriously make learning this so easy! Thank you
Great video!!! nice guide and outline for proofs. You should make more for theory and analysis.
Doing a group theory series this semester! ua-cam.com/play/PLL0ATV5XYF8B7YQ_nAPh-xiwXc2rVOQKx.html
Cool Thanks!
Thanks for the video! Just wondering why the ceilingfunction((2/ε)-1)
Did you figure it out? They're equal if we set epsilon = 1 correct?
I had the same question. Is there some reason epsilon cannot equal 1?
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.
Same question as well
@TT TT oh of course *facepalm. I appreciate that. I feel so silly for overlooking that 😂
Awesome breakdown, thank you!
Wow. This is the best explanation ever.
14:20 you assume that 0 js a natural number? If epsilon gets huge then the ceiling =0
How can i calculate n from step one if i have a factorial function, lets say i have n^2/n! assuming it's limit is 0
Great video, explained very thoroughly.
You are amazing!!!
amazing! Thank you.
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"
Like really........ The videos are amazing
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?
make more video ... I love it
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
That's how explaining a topic is supposed to be
Pleeasee make moree Proofs on Analysis!!!
5:12 isn't N a real number??
nope, natural number {1,2,3,4,5.......}
Very nice explanation
Thank you. Your explanation was thorough and very clear.
Excellent!
Angel, you are
damn, it doesn't get any clearer than this
So I can literally understand all of UA-cam 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!!
Great!!!!!!!!
legend
Thank you!
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.
Doesn't make any sense at all.
Excellent!
Excellent!