A sequence X = (x_n) in R is said to convert to x R. or x is said to to be a lim

Question

A sequence X = (x_n) in R is said to convert to x R. or x is said to to be a limit of (x_n), if for every > 0 there exists a natural number K N such that for all n greaterthanorequalto K, the terms x_n satisfy |x_n - x| 0 there exists a natural number K N such that for all n > K, the terms x_n satisfy |x_n - x| 0 there exists a natural number K N such that for all n > K, the terms x_n satisfy |x_n - x| 0, for every natural number K N, there exists n N such that n > K and the terms x_n satisfy |x_n - x| 0, there exists a natural number K N such that for all n greaterthanorequalto K, the terms x_n satisfy |x_n - x| 0, for all n N, the terms x_n satisfy |x_n - x|

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4. the proof an be stated in such a way that : If I give you an epsilon> 0, you have to
come up with an N that “works.” Also note that xn tends to x as n tends to infinity means the
same thing as mod(xn x) tends to 0 as n tends to infinity.

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