I wrote down my own proof of a well-known theorem in number theory but not sure if it's flawed or not: Theorem: There are infinitely many primes. Proof: Suppose there are finitely many primes. In that case, let P be the largest prime number and then P+1, P+2, ..., P+N (N is an integer that approaches infinity) are all non-prime numbers that are larger than P. Let X be the largest non-prime number that is obtained by multiplying all the non-primes larger than P and adding 1 or put into an equation as follows: X = P(P+1)(P+2)....(P+N) + 1 (N approaches infinity, of course). But this is a contradiction because X itself cannot be divided by any of P or P+1 or P+2 or P+N and therefore a new prime number that is larger than P.
@@wamyy5 Caltech taught you proofs well. I hated theoretical mathematical proofs because they're insanely hard but applied mathematics is more useful & tolerable.
@@wamyy5 Chemical engineering labs were a pain in the ass, no? I hated going to laboratories so science & engineering were not for me! But applied mathematics & other quantitative oriented non-lab courses like CS, economics, etc. were the best IMO.
Hi Angel thank you for your videos. Could you please make a video on when to take PSAT in high school. There are not many videos on this topic. Thank you in advance.
Hello! Unfortunately I wasn’t ever told the best time to take PSAT either, but my high school held the PSAT during my sophomore year in high school. I think you can take it anytime though! Sorry I couldn’t help much further :(
Hi, please check out my videos on how I got into Caltech (ua-cam.com/video/t0Lh7IWZqac/v-deo.html) and the things I didn't need to do to get into Caltech (ua-cam.com/video/Yz8xfqoC9Y0/v-deo.html)! Let me know if you have any specific questions you would like me to answer after watching :) Best of luck!
Wow, what a great place! Good luck in the summer!
Thank you!
You and Amy are always committed to providing useful information even though it is uncool and coolest thing to do.
I wrote down my own proof of a well-known theorem in number theory but not sure if it's flawed or not:
Theorem:
There are infinitely many primes.
Proof:
Suppose there are finitely many primes. In that case, let P be the largest prime number and then P+1, P+2, ..., P+N (N is an integer that approaches infinity) are all non-prime numbers that are larger than P. Let X be the largest non-prime number that is obtained by multiplying all the non-primes larger than P and adding 1 or put into an equation as follows: X = P(P+1)(P+2)....(P+N) + 1 (N approaches infinity, of course). But this is a contradiction because X itself cannot be divided by any of P or P+1 or P+2 or P+N and therefore a new prime number that is larger than P.
I've learned that proof before and I think that's right :)
@@wamyy5
Caltech taught you proofs well. I hated theoretical mathematical proofs because they're insanely hard but applied mathematics is more useful & tolerable.
@@wamyy5
Chemical engineering labs were a pain in the ass, no? I hated going to laboratories so science & engineering were not for me! But applied mathematics & other quantitative oriented non-lab courses like CS, economics, etc. were the best IMO.
Hi Angel thank you for your videos. Could you please make a video on when to take PSAT in high school. There are not many videos on this topic. Thank you in advance.
Hello! Unfortunately I wasn’t ever told the best time to take PSAT either, but my high school held the PSAT during my sophomore year in high school. I think you can take it anytime though! Sorry I couldn’t help much further :(
@@wAngel5 Thank you
I’m from the uk looking to apply to cal tech,is there any advice you could give me?
Hi, please check out my videos on how I got into Caltech (ua-cam.com/video/t0Lh7IWZqac/v-deo.html) and the things I didn't need to do to get into Caltech (ua-cam.com/video/Yz8xfqoC9Y0/v-deo.html)! Let me know if you have any specific questions you would like me to answer after watching :)
Best of luck!