Please Subscribe here, thank you!!! goo.gl/JQ8Nys Proof of Bernoulli's Inequality using Mathematical Induction
Пікірлер: 35
@melynx1159 Жыл бұрын
I'm so glad this channel exists. Despite my enormous passion for the subject, my maths skills mysteriously vanished during high school and I blame much to the overcomplicated way people teach in my country. This explanation is so easy that even a 6 years old kid could understand it. Thank you so much for allowing me to enjoy maths again! ❤❤❤
@benyoutube234 Жыл бұрын
I have been trying to find out why a>-1 and you are the only one who mentions it so thanks a lot.
@user-nf6rs2rh4u2 жыл бұрын
Thank you very much for this video. It was really useful to me. 👍🏼
@dangdangheather Жыл бұрын
literally the only video with an unknown im so grateful for you thankuuuuu
@TheMathSorcerer Жыл бұрын
😀
@dangdangheather Жыл бұрын
@@TheMathSorcerer :D
@forthrightgambitia10323 жыл бұрын
Nice. From this you can prove a series of inequalities that lead to the famous Gibbs inequality that is important in machine learning (which is why I was here).
@FadeStrategy3 жыл бұрын
Thank you so much.
@TheMathSorcerer9 жыл бұрын
@user-li6ev1ro9c4 жыл бұрын
Dude this is great. Love this vido
@TheMathSorcerer4 жыл бұрын
Thanks man!
@mantas98274 жыл бұрын
Thanks!!
@xJBRRR7 жыл бұрын
Can you tell me why ka^2 being greater than 0 enables us to drop the term?
@patricksalmas18777 жыл бұрын
So what he's basically doing is showing that, (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a + ka^2 >= 1 + (k + 1)a He never actually drops the ka^2, what he's really doing is saying that since we know ka^2 will be at least zero, we know that 1 + (k + 1)a will always be less than or equal to itself plus that ka^2. Since the we know that (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a + ka^2 (base on the induction hyp.). And we know that 1 + (k + 1)a + ka^2 >= 1 + (k + 1)a, we can then conclude that (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a, and that is what needed to be shown.
@davidfair48527 жыл бұрын
Awesome, thanks.
@Jazoopi4 жыл бұрын
@@patricksalmas1877 Godbless
@TheDropdeadZed4 жыл бұрын
If the LHS is greater than or equal to the RHS when ka^2 is part of the RHS, then the LHS will STILL be greater than or equal to the RHS when we make the RHS a bit smaller (since ka^2 is either 0, or it's a positive number). E.g. if LHS = 20, RHS = 10. We take away ka^2 = 2, so then RHS becomes 8. 20 is still greater than or equal to 8 so the statement is still true. I guess he didn't really 'take away' ka^2 since he didn't subtract it from both sides, essentially he just removed it from the picture since it didn't affect the inequality.
@jimallysonnevado39733 жыл бұрын
as an example 3+5>3 because 5 is positive we didnt really drop the 5 here
@shuvammitra8700 Жыл бұрын
Thank you so much
@ejsimon8138 жыл бұрын
thank you
@Medodell3 жыл бұрын
I see you used the theorem to prove it, I really do not get it
@chrysanthcrest7 жыл бұрын
Thank you!
@TheMathSorcerer7 жыл бұрын
np
@dragon-7511 Жыл бұрын
a is greater than -1 .why used ≥ this sign
@awesomecraftstudio9 ай бұрын
gotta love this shit
@CopryonАй бұрын
absolute chad
@bauyrzhankurmangaliyev3473 жыл бұрын
why it is not a>-1?
@iRealmath3 жыл бұрын
Some time ago I saw an article where a>-1 is taken instead of a=>-1. So I guess this guy had a mistake. (sorry for my English)
@isaactaremwa0014 жыл бұрын
Not so clear but thanks
@DarkOutsideNow4 жыл бұрын
Thank you for the video!!... Math: formulas written by people who are lazy, so they short handed everything into hard-to-understand formatting that requires formal education. Sometimes without knowing what level or type of math that's applied, it becomes hard to provide the answer. Suppose x + y = (x+y) is true. prove it. AHH!! Which way?!?! Elementary school style (count those apple, oranges, which are all fruits) or advanced math using proofs that take 10x longer? (Edit for slight grammar issue)
@somiechannel74072 жыл бұрын
❤️❤️❤️
@oneaboveall62394 жыл бұрын
well i understand Bernoulli's Inequality but i still hate pure math
@energy-tunes Жыл бұрын
where numbers
@maxpercer71192 жыл бұрын
gets a little murky the logic dealing with the sign of (1+a ) at 3:45 , kind of reverse logic. see math.stackexchange.com/questions/181702/proof-by-induction-of-bernoullis-inequality-1xn-ge-1nx Nice video, i am hooked to math (and your videos).