I need to prove that 1/n has a limit of zero using the following definition:
The statement that the point sequence p1, p2, . . . converges to the point x means that if S is an open interval containing x then there is a positive integer N such that if n is a positive integer and n ≥ N then pn ∈ S.
The statement that the sequence p1, p2, p3, . . . converges means that there is a point x such that p1, p2, p3, . . . converges to x.
the instructor was adamant that we are not to use epsilon delta in these proofs for our text does not use such notions. But I am at a lost as to how we prove it without them. Do I just substitute a different variable in the epsilon and delta places? Any advice on how to get started would be appreciated.
The Attempt at a Solution
This is my second attempt in a real analysis class :( It is amazing how different the material is from course to course even for the same course.