Proof: Limit Law for Product of Convergent Sequences | Real Analysis

[@MajesticQT]

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

[@WrathofMath]

Thank you for watching, glad to help!

[@modernfreeman4228]

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!

[@jingyiwang5113]

You really such a wonderful video explaining this knowledge point. I am really grateful for your explanation! It helps me a lot!

[@WrathofMath]

Thanks so much, glad to hear it!

[@wtt274]

Thank you sir for your great video .Your explanations are exceptionally clear !

[@WrathofMath]

Thank you for watching!

[@jadekan72]

This is absolutt amazing! It helps so much! Great jobb! Thank you sir! :D

[@rahu6730]

Nicely explained. Thanks

[@WrathofMath]

Glad to help - thanks for watching!

[@juanfelipequinterovanegas4479]

Thank you. It was very intuitive!!

[@WrathofMath]

You're welcome - glad it was clear! If you haven't already, check out my Real Analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Working on many more analysis lessons!

[@Redoni04]

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.

[@WrathofMath]

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?

[@berlinisvictorious]

Real question, I am bad at inequalities, what property is this: if |b_n| ≤ C and |b_n||a_n - a|

[@bhavayluthra2381]

Why did you chose |an-a|

[@dabeerahmed4802]

because c can be 0, and need to avoid division with 0

[@dhruw9935]

Wild proof imo😢😮

[@samuelhawksworth1923]

If we set the denominator to 2a+1 if a=0 wouldnt we get E/1+E/1 which gives 2E?

[@danconohan1524]

Saw the same thing. Isn't 2a+2 better?

[@GameHorizons.]

if a = 0,while thing equals to zero

[@itisonlykevin3676]

i dont care what you say this is some pure black magic ( understood every thing btw)

[@karthikkeys555]

Which app u used for writing sir

[@bbtc1558]

Thank u sir for great explanation

[@turokg1578]

wish i was this good at analysis lol...

[@niranjanca3534]

Thank u very much sir.....

[@WrathofMath]

You're very welcome! Thanks for watching and check out my analysis playlist if you are looking for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@evaofficial8335]

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 :)

[@oscarlin8450]

Thank you

[@WrathofMath]

You're very welcome, thanks for watching! If you're looking for more real analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@neevetiasli]

Sir you sounded like sheldon cooper

[@zurollo3276]

Big brain

[@WrathofMath]

Nothing like a quality big-brain proof! Have you seen my calculus raps? I think they're exceptionally big-brain kzbin.info/www/bejne/n4SVaJWZhJeEo5o