I want you to know that I genuinely believe you're the best instructor of real analysis I've ever come across. Your ability to explain complex concepts with clarity and your dedication to helping students understand the material are truly remarkable. Thank you for making such great videos.
Does this definition mean that there are infinitely many accumulation points when A is a subset of the natural numbers? (Since we say there exists y in A, then n=1,2,3,4,5,6,... would only require finitely many elements of N in the sequence). I am currently enrolled in elementary real analysis, so I am sorry if my comment makes no sense, still learning the basics! PS. I really appreciate your style of teaching. Love the examples! You should totally set up a patreon!
Yes! This is one of the key elements of the definition. For example, A = (0,1) has 0 and 1 as accumulation points. Some sets *do* contain all their accumulation points - these are **closed** sets.
You are amazing. This is the most understandable and wonderful analysis and topology lessons I have ever watched.
I want you to know that I genuinely believe you're the best instructor of real analysis I've ever come across. Your ability to explain complex concepts with clarity and your dedication to helping students understand the material are truly remarkable. Thank you for making such great videos.
Thank you!
I testify to that also. How i wish you were my analysis lecturer. Thank you and may Almighty Allah bless you.
OMG your videos are so helpful Matthew, I am a real analysis student and I can't believe I have benefited so much that I did from my lectures
Great explanations 🎉,,,
Does this definition mean that there are infinitely many accumulation points when A is a subset of the natural numbers? (Since we say there exists y in A, then n=1,2,3,4,5,6,... would only require finitely many elements of N in the sequence).
I am currently enrolled in elementary real analysis, so I am sorry if my comment makes no sense, still learning the basics!
PS. I really appreciate your style of teaching. Love the examples! You should totally set up a patreon!
These videos are so helpful - ty
can an accumulation point be outside a Set?
Yes! This is one of the key elements of the definition. For example, A = (0,1) has 0 and 1 as accumulation points. Some sets *do* contain all their accumulation points - these are **closed** sets.