I think there’s something I don’t get about limit points. In the beginning everything was clear but approaching the end everything looked blurr. I don’t know what I don’t understand but I know there’s something I’m not getting with the concept of limit points
@@SkanCityAcademy_SirJohn and that's the corollary to the bolzano wierstrass theorem. That if an infinite set is bounded that there at least a limit point. Which can be found by considering the deleted delta neighbourhood of the point in claim as a limit point if the open interval contains members of the set
The answer is right at the onset. The theorem specifies that delta should be greater than zero. So delta can be 0.1, 0.2, 0.3 etc So assuming delta is 0.1. Then we want to say that the intersection of S and (a-0.1, a+0.1) contains infinitely many points. Between a and a+0.1 which is the region of intersection, we can have for example, a + 0.001 a + 0.002 . . . . . And on and on
kindly take notice of the fact that some infinite sets are bounded, others are not. In addition to that you should know that every bounded infinite set has at least a limit point.
God bless you so much.You just explained to me in just minutes what I had been surfing you tube for hours to understand .Amazing work👏👏👏
Youre most welcome
May God richly bless you. You may not know how you have helped us. Especially those of us from KNUST.
awww Amen. and thanks so much
Thank you so much may God bless you you are such a good teacher ❤
thanks so much
Thanks for the video! 😊
Most welcomed
Keep helping us, man🙌
thanks so much
God bless you abundantly
Amen...
superb, thank you
You are most welcome
I think there’s something I don’t get about limit points. In the beginning everything was clear but approaching the end everything looked blurr. I don’t know what I don’t understand but I know there’s something I’m not getting with the concept of limit points
Wow...okay. So you know, can you do me a favour by going back, to watch the video all over again. If you still dont get it let me know, please
Wow... Okay, you know. I want you to do me a favour by going back to watch the video a second time. If you atill dont get it. Please let me know
Skan city Yahweh bless you
thanks so much.
i'm your new follower.
Thanks so much
On point! Keep it up!😁 could you try a background that is a bit less bright? like ash or black or something?
oh okay, will try that other backgrounds and see... are you having challenges with the background?
Thank you SkanCity🙌, Any group I can join to access your videos easily?
which school do you attend?
@@SkanCityAcademy_SirJohn KNUST
Amazing😭😭😭
Thanks so much
So for a number to be a limit point it shouldnt necessarily be part of the interval. Right?
Yes, it should not necessarily be in the set. Limit point, basically indicates where the set or sequence is approaching.
You should also work on the adds which keeps on appearing
okay, thank you...
Is the deleted delta neighbourhood or the delta neighbourhood
Kindly come again with your question?
@@SkanCityAcademy_SirJohn I'm saying it's rather the deleted delta neighbourhood not the neighbourhood per say.
@@SkanCityAcademy_SirJohn and that's the corollary to the bolzano wierstrass theorem. That if an infinite set is bounded that there at least a limit point. Which can be found by considering the deleted delta neighbourhood of the point in claim as a limit point if the open interval contains members of the set
Oh okay noted. Thanks so much, kindly indicate the time in the video, I will check and acknowledge
@@SkanCityAcademy_SirJohn the definition was in 0:20seconds
It seems I'm confused with the example two😢😢
Really, please what's the confusion
Sir...what are the limit points of the set {cosn: n is any natural number}?
Its the closed interval [-1,1]
@@SkanCityAcademy_SirJohn Sir then...Are the limit points of the set {cosn: n is natural no} same as the limit points of the sequence {cosn}?
Yes
From 0-359, the cycle begins again from 360-719 .....
"now, what this primarily means is that...."😂😂😂
Hahahaha
Without any given value for delta, how did you know that there would be infinitely many solutions between 0 and delta
The answer is right at the onset.
The theorem specifies that delta should be greater than zero. So delta can be 0.1, 0.2, 0.3 etc
So assuming delta is 0.1.
Then we want to say that the intersection of S and (a-0.1, a+0.1) contains infinitely many points.
Between a and a+0.1 which is the region of intersection, we can have for example,
a + 0.001
a + 0.002
.
.
.
.
.
And on and on
Thank you very much
And when do we say it doesn’t have many solutions please
I think that is in the next video
Same here
why is it that an infinite set has sometimes a limit point and other times it doesnt that what I dont get
kindly take notice of the fact that some infinite sets are bounded, others are not. In addition to that you should know that every bounded infinite set has at least a limit point.
@@SkanCityAcademy_SirJohn , does it mean unbounded infinite sets have no limit points?
@@KingsleyRobertson yes