I love when a deep result in mathematics is provable only with elementary techniques, like basic knowledge of combinatorics and arithmetic.
In this video I will present the queen of this proofs, namely the Erdős' proof of the Bertrand's postulate, which states that it is always possible to find a prime number between a positive integere n and 2n.
In general such kind of results about primes requires a large amount of difficult techniques, from complex to Fourier analysis and so on.....but today we will show how imagination can lead us to a beautiful journey inside prime numbers!
I will review every step of his proof, which in my opinion is very creative and ingenious.
Do you know other marvellous elementary proofs? Let me know in the comments 😎
I apologize for the bad english but I have to admit that I'm italian, so maybe it is understandable 😜
❗❗❗ DISCLAIMER: at about 17:20 I use the bound 4^x and not 4^(x-1). This is in fact a weaker bound than the one given by the third key lemma, but I will use it anyway only because I want to speak about the Landau's trick, which works very well in the range of primes in [2,4001]. ❗❗❗
For other videos in English look at the following playlist:
ru-vid.com/group/PLuyidMWlEjrqmoFTxxig33J2IOeZItrzK
------------------------------------------------
00:00 Introduction
01:44 Proof of First Lemma
04:50 Proof of Second Lemma
09:18 Proof of Third Lemma
12:50 Final proof+Landau's trick
19:25 Conclusion
------------------------------------------------
#3Blue1Brown #SoMe1
22 авг 2021
