Thanks for sharing your solution! Unfortunately, 🤔 I don't follow 🤔 i think that you can choose p and q such that n^2 > 2. But i am not sure, i am a little confused by the definition of n, is it n= p/q + pq/4 or is it n=p/q + 1/(4pq) or is it n=p/q+q/(4p) or something else? It might work though! i will need to think about it more! Thanks again!
@@academyofuselessideas Let A = {m in Q such that m^2 < 2} I showed that this set doesnt have maximum. Suppose m = p/q is the maximum. We have m^2 p^2 < 2q^2 If n= p/q + 1/(4pq) n^2 = p^2 /q^2 + 1/(2q^2) + 1/(4pq)^2 It is clear that 1/2 + 1/(4p)^2 < 1 p^2/q^2 +1/(2q^2) +1/(4pq)^2 < 2 --> (p/q+1/(4pq))^2 < 2 Then m
@@Miguel14159 thanks for the detailed explanation... cool! i think that in the first message, the parenthesis 1/(4pq) would be helpful! (maybe you can still edit it?) Anyways, the explanation is pretty informative... thanks!
😅 I blame your professor! Rudin is a decent good if you have someone explaining the motivations and ideas behind the topics... Luckily now you can get a lot of great insights from people online! (A few years ago, professors were the only source of information which made learning a bit harder!) I like Real analysis by Jay Cummings because he gives a lot of motivations and the writing is very friendly for self study (just in case you still want to learn the topic). Also feel free to ask if you have any question, I may not know the answer but sharing your pain sometimes helps!
@@academyofuselessideas i did like rudins book, my prof just didn’t go into motivations just straight into proofs. I hate saying it but he was not a good teacher. Otherwise it was so cool to learn about infimum,supremum, Archimedes principle. One day I will do the textbook on my own 🤞😁
@@erythsea Oh, feel free to ask for any help you may need reading it... I have thought about giving a series of streams on analysis, but I am not sure if i will ever do
![sin x + cos x =1 Solved [ IB Math]](/img/n.gif)
I am also difficult and lacking motivation which is why i love Baby Rudin
🤣
Nega You is just Me, thank you!
we all are Nega you sometimes! (though, maybe I should include Nega Slim as a character too)
Math being hard is not a bug; it is a feature.
amusing perspective... thanks for sharing it!
I just read 3 chapters of Baby Rudin, and I am beginning to ask questions myself. "Why am I punishing myself with pure mathematics?"
If it feels like punishment, i would say, Don't do it... but as self punishment goes, math is not the worst
Perhaps you have discovered that you are a masochist. Once again, math is teaching us about ourselves!
@@covariance5446 🤣🤣🤣
Assume a maximum exists, let m = p/q be that max number.
pick n = p/q + 1/(4pq)
notice that n^2 < 2 and m < n. Contradiction.
Thanks for sharing your solution!
Unfortunately, 🤔 I don't follow 🤔 i think that you can choose p and q such that n^2 > 2. But i am not sure, i am a little confused by the definition of n, is it n= p/q + pq/4 or is it n=p/q + 1/(4pq) or is it n=p/q+q/(4p) or something else? It might work though! i will need to think about it more! Thanks again!
@@academyofuselessideas
Let A = {m in Q such that m^2 < 2}
I showed that this set doesnt have maximum. Suppose m = p/q is the maximum.
We have m^2 p^2 < 2q^2
If n= p/q + 1/(4pq)
n^2 = p^2 /q^2 + 1/(2q^2) + 1/(4pq)^2
It is clear that
1/2 + 1/(4p)^2 < 1 p^2/q^2 +1/(2q^2) +1/(4pq)^2 < 2
--> (p/q+1/(4pq))^2 < 2
Then m
@@Miguel14159 thanks for the detailed explanation... cool! i think that in the first message, the parenthesis 1/(4pq) would be helpful! (maybe you can still edit it?) Anyways, the explanation is pretty informative... thanks!
Great video, my real analysis prof used this textbook. I dropped the course 😎💪
😅 I blame your professor! Rudin is a decent good if you have someone explaining the motivations and ideas behind the topics... Luckily now you can get a lot of great insights from people online! (A few years ago, professors were the only source of information which made learning a bit harder!)
I like Real analysis by Jay Cummings because he gives a lot of motivations and the writing is very friendly for self study (just in case you still want to learn the topic). Also feel free to ask if you have any question, I may not know the answer but sharing your pain sometimes helps!
@@academyofuselessideas i did like rudins book, my prof just didn’t go into motivations just straight into proofs. I hate saying it but he was not a good teacher. Otherwise it was so cool to learn about infimum,supremum, Archimedes principle. One day I will do the textbook on my own 🤞😁
@@erythsea I am looking forward to read your book! or at least your writting on those subjects (or any other subject you decide to write about!)
@@academyofuselessideas haha I’m not smart enough to write math textbook. I meant go through baby rudin on my own 😁
@@erythsea Oh, feel free to ask for any help you may need reading it... I have thought about giving a series of streams on analysis, but I am not sure if i will ever do