This proof uses only elementary properties of algebra and a cool induction idea
Пікірлер: 18
@tigeronionАй бұрын
The famous Cauchy proof. Nice!
@Jancel70515 сағат бұрын
great proof, i think you forgot to set X to min({a}_{n+1}^{2^\alpha}) to ensure boundedness tho
@MyOneFiftiethOfADollar Жыл бұрын
Liked the how you "filled in the gaps" between powers of 2 informally, before you got to the formality of the induction proof.
@williampluim844Ай бұрын
You're a beast. Thanks!
@samkerr18267 ай бұрын
This guy is the Hans Neimann of Maths
@dddddd-jj5md2 ай бұрын
lol
@user-tv3lc6eu2y2 жыл бұрын
My favorite proof uses Jensen's inequality (applying to concavity of ln x)
@ShefsofProblemSolving2 жыл бұрын
Oh that's actually pretty cool
@ahmedlutfi48948 ай бұрын
wow the explanation is making alot of sense there is no blank spaces while following up
@kenchen91982 ай бұрын
thanks,this video helps me a lot❤
@thealgebraicadventures-bz6pz3 ай бұрын
13:00 nice technique 😃
@user-qi4fq3gz6d6 ай бұрын
can you help?...when should we use iff symbol in our maths equation or proof etc
@thedeathofbirth0763 Жыл бұрын
Can you make another video and explain the general case a bit more in detail please. I could follow your reasoning till the general case. I really want to understand this. Thank you. Why the last term wasn't raised to (1/2^a) for instant?! Why you took n< 2^a in the first place, because to me it won't make it the general case but for the number of elements to be powers of two!
@ShefsofProblemSolving Жыл бұрын
We showed AmGm for all powers of two. Now the general case is that we take an n that's not a power of 2 and let is be less than some power of two. Now we take the thing we knew for powers of two that holds true and show that if we plug in a couple of identical values we'll get the inequality for n. That's the idea
@thedeathofbirth0763 Жыл бұрын
@@ShefsofProblemSolving I see, thank you for the time you took to explain it more clearly.
@darcash17383 ай бұрын
I never heard of em then I suddenly had to prove it 😂