I was able to fully grasp the Epsilon-delta proof but with the Epsilon-Natural number limit proof for sequence, I'm facing some confusion as regards the "idea".
So by the definition of Epsilon-Natural number limit proof:
For each Epsilon greater than zero, there is an n greater or equal to N such that |x_n - L| < epsilon.
If someone could explain to me the significance of this N and it's relation to the proof, that would be great!