It's a course in real analysis and we are on sequences. The definition of the limit of a sequence follows:
e = epsilon
A sequence X=(xsubn) in R (real) is said to converge to x in R, or x is said to be a limit of (xsubn), if for every e > 0 there exists a natural number K(e) such that for all n>=K(e), the terms xsubn satisfies | xsubn - x | < e
I am KINDA getting it but then i am not 100% sure. I know that I will use this definition through the rest of the chapter so I want to clearly understand it before moving on. I understand that basically if any e > 0 is picked, the difference between the limit x and the value xsubn would still be smaller than that epsilon that was picked. This pretty much gaurantees that xsubn and x are so closed that x must be the limit. But what is the deal with picking K???
e = epsilon
A sequence X=(xsubn) in R (real) is said to converge to x in R, or x is said to be a limit of (xsubn), if for every e > 0 there exists a natural number K(e) such that for all n>=K(e), the terms xsubn satisfies | xsubn - x | < e
I am KINDA getting it but then i am not 100% sure. I know that I will use this definition through the rest of the chapter so I want to clearly understand it before moving on. I understand that basically if any e > 0 is picked, the difference between the limit x and the value xsubn would still be smaller than that epsilon that was picked. This pretty much gaurantees that xsubn and x are so closed that x must be the limit. But what is the deal with picking K???
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