Suppose that the function f is defined only on the integers. Explain why it is continuous.
The ε/δ definition of continuity at a point c:
for all ε > 0, there exists a δ > 0 such that |f(x) - f(c)| ≤ ε whenever |x - c| ≤ δ
The Attempt at a Solution
I understand this completely when we are defining our function on ℝ. I can't intuitively understand this for the integers. I am thinking that if we choose δ = 1, that somehow guarantees that |f(x) - f(c)| will be small enough, but I'm not sure of this because my intuition is stuck in the reals.