Hi, I'm having difficulty understanding this definition.

A sequence

http://upload.wikimedia.org/math/8/f...d7e81e87d7.png of real numbers is calledCauchy, if for every positive real numberε, there is a positive integerNsuch that for all natural numbersm,n>N

|xm-xn|< ε

It seems simple, but the point I don't understand isN.What is it? What is the function of it?

I'll be grateful if you could explain this to me. Thanks in advance!