An infinite sequence of numbers {a_n} has a limit L if, no matter how small a number ϵ > 0 you choose, from a certain n onward the absolute difference |L−a_n| between L and a_n is always greater than ϵ.

An infinite sequence of numbers {a_n} has a limit L if, no matter how small a number ϵ < 0 you choose, from a certain n onward the absolute difference |L−a_n| between L and a_n is always less than ϵ. 

An infinite sequence of numbers {a_n} has a limit L if, no matter how large a number ϵ > 0 you choose, from a certain n onward the absolute difference |L−a_n| between L and a_n is always less than ϵ. 

An infinite sequence of numbers {a_n} has a limit L if, no matter how small a number ϵ > 0 you choose, from a certain n onward the absolute difference |L−a_n| between L and a_n is always less than ϵ.