Great, I understood everything, I must accept that the first direction of the proof was not so clear, but with time I got it. And the reciprocal was easy for me, God bless you Gandalf jajaja
Hey, The Math Sorcerer I have a question. At (2:10), you wrote there exist x is not in A, s.t x is a limit point. x is a limit point of what? Do you mean limit point of A?
It's weird, never seen anyone do any concrete examples of this, they just go through the proof. Could you please do an example? For example for the subset {(x, y) in R^2 | x^2+xy+y^2 = 4}.
hey! im just starting my studies in basic topology (with baby rudin). and i cant visualize what is a limit point. Do you have any intuitive way of understanding this concept? thanks
I think of a *limit point of a set A* as a point that is "really REALLY close" to the set A; for example, in the case of a metric space, say X, you'd have that a limit point x of the subset A of X follows that d(x,A)=0 ("the distance of x to A" is the smallest possible). Remember that "the distance of a point y in X to the subset B of X" is d(y,B):=inf{d(y,z) : z is in B}
Im studying limit point of an interval, this method also seems applicable when it comes to an interval (the proof given by my tutor was too complicated
I remember a related concept of "adherent points". A set is closed iff it contains all its adherent points. The proof is almost the same. I think the only real difference is when it comes to the singleton set, {x}.
@@TheMathSorcerer One thing that was frustrating for me as a student was when I went to the library to get a supplimental explanation for a concept that I was having trouble understanding from the lectures and the textbook, I found that other authors would give "equlivant" definitions of the same concepts. What was a definition in our textbook was a theorem in the library book and vice versa. A => B => C => A. We go around in a circle. Pick your definition, A, B, or C. Then prove the other two.
@@OleJoe omg yes!!!!!!!! I totally agree this happens so much especially in proof based mathematics. It's constant and it is unfortunate. I remember this happening with my definition of limsup and liminf, ahh so many different definitions:)
![How to Prove that the Interval (a, b] is Not an Open Set](http://i.ytimg.com/vi/aAYMxtLjNc0/mqdefault.jpg)
You're my hero. It's been very difficult finding help in analysis and topology
Great, I understood everything, I must accept that the first direction of the proof was not so clear, but with time I got it. And the reciprocal was easy for me, God bless you Gandalf jajaja
Hey, The Math Sorcerer I have a question. At (2:10), you wrote there exist x is not in A, s.t x is a limit point. x is a limit point of what?
Do you mean limit point of A?
It's very helpful 🇮🇳🙏
Thank you so much!!!! you helped me a lot
Glad I could help!
It's weird, never seen anyone do any concrete examples of this, they just go through the proof. Could you please do an example? For example for the subset {(x, y) in R^2 | x^2+xy+y^2 = 4}.
hey! im just starting my studies in basic topology (with baby rudin). and i cant visualize what is a limit point. Do you have any intuitive way of understanding this concept? thanks
I think of a *limit point of a set A* as a point that is "really REALLY close" to the set A; for example, in the case of a metric space, say X, you'd have that a limit point x of the subset A of X follows that d(x,A)=0 ("the distance of x to A" is the smallest possible). Remember that "the distance of a point y in X to the subset B of X" is d(y,B):=inf{d(y,z) : z is in B}
Could you possibly make a video on how to formally prove that the set given by U = [0, 1) ∪ [2, 3] is not compact. Thanks in advance.
It’s very helpful!
Im studying limit point of an interval, this method also seems applicable when it comes to an interval (the proof given by my tutor was too complicated
thank you!
I don't get the definition of the limit point!
I remember a related concept of "adherent points". A set is closed iff it contains all its adherent points. The proof is almost the same.
I think the only real difference is when it comes to the singleton set, {x}.
yeah!! adherent points are points in the closure, very very similar definition, almost the same but they are not:)
@@TheMathSorcerer One thing that was frustrating for me as a student was when I went to the library to get a supplimental explanation for a concept that I was having trouble understanding from the lectures and the textbook, I found that other authors would give "equlivant" definitions of the same concepts. What was a definition in our textbook was a theorem in the library book and vice versa. A => B => C => A. We go around in a circle. Pick your definition, A, B, or C. Then prove the other two.
@@OleJoe omg yes!!!!!!!! I totally agree this happens so much especially in proof based mathematics. It's constant and it is unfortunate. I remember this happening with my definition of limsup and liminf, ahh so many different definitions:)