Would N=infinity work?
Yes, when it's coutably infinite, as Cantor said.
Imagine you have a (countable) infinite number of bikes, all lined up. Then you move them all up a place so the first place is empty and you add one to the start. You still must have the same number of bikes otherwise you'd not have had a coutable infinite number of bikes in the first place.
A similar argument goes for pieces of cake all lined up. You can eat as many as you like (finite number) and still have an infinite number left.