Use the definition of pointwise convergence carefully....carefully!!! I almost did it in this video but I didn't want to make it to Long...maybe I will do more like this. Thanks for your comment!!!
Given that we look at x>0, the condition 0 1. Is my intuition correct, and would it be appropriate to say that n*x -> 1 because x is getting squashed toward 1/n as n->inf ?
Here, x is always treated as a *fixed* value between 0 and positive infinity. It never gets squashed to anything. Maybe you can think about it like this: Choose an arbitrary value for x>0 and fix it. Now, look at the case that 00. But why? Can we really find a natural number n_0 so that x>1/n for all n>n_0? The answer is yes. This is a consequence of the Archimedean property (see en.wikipedia.org/wiki/Archimedean_property) stating that for any positive real number x, there exists a natural number n so that x>1/n. Hope this helps!
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Nicely explained sir
Thanks a lot for this video:)
But one question how would I prove this formally, any hints would be appreciated. Thanks again
Use the definition of pointwise convergence carefully....carefully!!! I almost did it in this video but I didn't want to make it to Long...maybe I will do more like this. Thanks for your comment!!!
Thanks , keep up the great work💪💪🧙🏽♂️
Thank you very much for such a great explanation👍
THANK YOU SIR!😊
Welcome 😊
Appreciate the math love. Keep it coming.
❤️❤️
Given that we look at x>0, the condition 0 1. Is my intuition correct, and would it be appropriate to say that n*x -> 1 because x is getting squashed toward 1/n as n->inf ?
Here, x is always treated as a *fixed* value between 0 and positive infinity. It never gets squashed to anything. Maybe you can think about it like this: Choose an arbitrary value for x>0 and fix it. Now, look at the case that 00.
But why? Can we really find a natural number n_0 so that x>1/n for all n>n_0? The answer is yes. This is a consequence of the Archimedean property (see en.wikipedia.org/wiki/Archimedean_property) stating that for any positive real number x, there exists a natural number n so that x>1/n. Hope this helps!
Great explanation, Sir!
Can I propose a problem to you and then you solved it in your video, Sir?
4:05 i related to that laugh so much and i dont know how to put it into words why i did
Sir i have a question but thats not related to this video, i think, i be able to ask that where are you from? also are you professor which university?
「上記のギフトのいずれかを選択できます」、
Excellent video! But dear god invest in a real eraser.
thanks! I know right:)
Saya tidak percaya ia boleh menjadi sebaik ini