Proof: Limit Law for Product of Convergent Sequences | Real Analysis
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- čas přidán 26. 08. 2024
- We prove the limit law for the product of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n*b_n converges to a*b. As in, the product of convergent sequences converges to the product of their limits. This is a slightly tricky proof using the epsilon definition of a convergent sequence, and absolute value manipulations!
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I’m currently in calc 1 and struggling a lot, but anytime I need help with a proof I see your videos and they’re always great, so thank you
Thank you for watching, glad to help!
Wow this is amazing, I was struggling with the last step, couldn't figure out what happened to the 1 added in the denomitor but now it makes perfect sense. Thank you!
You really such a wonderful video explaining this knowledge point. I am really grateful for your explanation! It helps me a lot!
Thanks so much, glad to hear it!
Thank you sir for your great video .Your explanations are exceptionally clear !
Thank you for watching!
Real question, I am bad at inequalities, what property is this: if |b_n| ≤ C and |b_n||a_n - a|
This is absolutt amazing! It helps so much! Great jobb! Thank you sir! :D
Thank you. It was very intuitive!!
You're welcome - glad it was clear! If you haven't already, check out my Real Analysis playlist: czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
Working on many more analysis lessons!
Nicely explained. Thanks
Glad to help - thanks for watching!
Thank u sir for great explanation
Wild proof imo😢😮
Why did you chose |an-a|
because c can be 0, and need to avoid division with 0
wish i was this good at analysis lol...
sir, sorry to disturb you again but cant help it.
your way of teaching is just amazing NGL
so I need your help to solve this particular question which is again from group theory
Identity element of the binary operation ∗ on G = {(a,b) / a,b ∈ R, 𝑎≠ 0}, defined by (a,b) ∗ (c,d) = (ac , bc +d) , will be __
Select one:
a. (2,2)
b. (1,0)
c. (0,1)
d. (0,0)
please explain me how to solve them also possible make a video out of it whenever you can
and yeah on a serious note, thank you so much for your assist :)
Thank u very much sir.....
You're very welcome! Thanks for watching and check out my analysis playlist if you are looking for more! czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
If we set the denominator to 2a+1 if a=0 wouldnt we get E/1+E/1 which gives 2E?
Saw the same thing. Isn't 2a+2 better?
Thank you
You're very welcome, thanks for watching! If you're looking for more real analysis, check out my playlist! czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
Which app u used for writing sir
Can somebody help me understand what he did at 12:40 because i just can't make sense of this no matter how much i think about it.
Thanks for watching and sure thing, that's a tricky step. I tried to explain it intuitively but I regret not also writing out the math to prove that step as that would have helped.
Let's first look at cε/(2c+1). If we reduce the denominator, then certainly our number becomes bigger. In general, a/(b+1) < a/b. Just like 2/4 < 2/3. So we have cε/(2c+1) < cε/2c. Then, cε/2c = ε/2. Similar logic will suffice for the second expression with |a| as well. Does that help?
Big brain
Nothing like a quality big-brain proof! Have you seen my calculus raps? I think they're exceptionally big-brain czcams.com/video/iS27bcO2Qm8/video.html