Why epsilon is 1/2? why n>=n(here, n is a natural number)?

epsilon is taken upto our choice.... if we have to disprove something, then in that case we take such epsilon value that helps us in disproving it....but in case of proving somethi...

we take epsilon such that , that epsilon can dispoove the given statement

here epsilon equals to 1/2 has been taken...but if you choose any positive value of epsilon less than 1, it will work

€>0 (i.e any positive no. (it is not compulsory that € is fixed , we choose € according to our requirement ) (as you seen in various theorem or concept of limit point) n is natural...