Every time I search for an explanation on a topic of Analysis or Linear Algebra I found a video of yours and I end up understanding it. Huge thanks! I appreciate your work and your enthusiasm :D
Here's a nice exercise to do afterwards: Prove the same is true for the product of two sets and then try and show the real numbers are a field using the fact that the rational numbers are. (If the field thing is too hard just show that the real numbers are closed under +,-,x, and / by non zero denominators)
Thank you for uploading Prof. Peyam. I was inspired by your density of Q video so I challenged myself to come up with a proof before I watched this one. What I thought about was that if the sup(A+B) is different (and therefore strictly less than) supA+supB (because it is an upper bound of A+B), then there would be numbers between them of the form a+b which leads to a contradiction. So I invoked the density of Q to say there is a rational r such that sup(A+B)
You are great!! I' m currently studying Analysis with Abbot Understanding Analysis, and this thing appears as an exercise. I didn't can solve they, and you show me my possible mistake was not consider Sup (A) -b as an upper superior bound
Hi, Dr Peyam. I am currently a bit confused about the concept of sup. In set theory, I learned that if B is a subset of A, then “sup(B) in A” is a∈A such that b
Dr Peyam thank you, just watch your recommended video and another one about sup. But I think your definition has some connection with the set theory one.
Every time I search for an explanation on a topic of Analysis or Linear Algebra I found a video of yours and I end up understanding it. Huge thanks! I appreciate your work and your enthusiasm :D
Loving the in depth analysis series
Thank you!!!
Here's a nice exercise to do afterwards: Prove the same is true for the product of two sets and then try and show the real numbers are a field using the fact that the rational numbers are. (If the field thing is too hard just show that the real numbers are closed under +,-,x, and / by non zero denominators)
Following exactly what you said in 4:28 but using symbols could we make the next deduction. From a+b
sup(sup(A)+sup(B)) doesn’t really make sense. supremum works for sets, not numbers
@@drpeyam Thank you - yes that makes absolute sense.
You should be our college professor. Because he always choose the same way what is written in his notebook which is so boring.
Awww thank you!!
This made me finally comprehend this concept. Amazing video !!
Loved the way you proved sup(A+B) >= sup(A) + sup(B), so easy to follow
Thank you for uploading Prof. Peyam. I was inspired by your density of Q video so I challenged myself to come up with a proof before I watched this one. What I thought about was that if the sup(A+B) is different (and therefore strictly less than) supA+supB (because it is an upper bound of A+B), then there would be numbers between them of the form a+b which leads to a contradiction. So I invoked the density of Q to say there is a rational r such that sup(A+B)
Such a beautiful steps from you. Thanks professor pyeam ❤️❤️❤️ 10:59
Hello thanks for the effort, I have a small question please... What ARBITRARY means ?
Love your enthusiasm. Thanks!
You are great!! I' m currently studying Analysis with Abbot Understanding Analysis, and this thing appears as an exercise. I didn't can solve they, and you show me my possible mistake was not consider Sup (A) -b as an upper superior bound
Hi, Dr Peyam. I am currently a bit confused about the concept of sup. In set theory, I learned that if B is a subset of A, then “sup(B) in A” is a∈A such that b
No it’s a different sup
Supremum of a set ruclips.net/video/lZEcsOn6qUA/видео.html
Dr Peyam thank you, just watch your recommended video and another one about sup. But I think your definition has some connection with the set theory one.
They do sound similar, I have to admit
Just loved this video. It cleared my confusion
Dr Peyam, what about a number theory series ?
I know 0 number theory
You're A good teacher, thank you.
Thank you :)
holy shit that’s a beautiful proof.
Thank you Dr ... the proof is very clear and understandable
Beautifully explained.thank you sir.😊
What a nice explanation!!!
Thank you so much sir.
Analysis video, here we are :)
great video please keep doing more
I liked very much the way you analyzed the equation . I would like to thank you very much for this effort 🙏🙏🙏🙏👍👍👍💪
It's really fun☺☺
Good video, thanks!
Who is here from Tyler1?
What Sup? :)
U are a lifesaver
great! greetings from Brazil....
The reverse direction is a miracle. Thank you.
Challenge : is there a set with a solution to sqrt(x) = -1 ?
Yes. An empty set. Sqrt(x) is by definition always positive. If you change the definition to be the same as power of 1/2, the answer is then {1}
nice video thanks
Assisti sem ser fluente em inglês e ainda assim achei super fácil entender, parabéns
Obrigado 😌
That's pretty clever!
Thank you !!!!
thank you :)
Really nice proof
THANK YOU!
Thankyou Sir
then the problem is me 🙂
You showcase the fun and profound beauty of analysis so well!