Explain precisely why sequence $a_n = n $ is (not) continuous and differentiable.
I have given this problem some thought and come up with the following answer: A sequence is continuous but is not differentiable.
Continuous:
Consider a function $f:\mathbb R \to \mathbb R$ given by $f(x) = x$. Now consider $f \upharpoonright \mathbb N$ This is exactly the sequence in question and it's continuous because if we restrict the domain of a continuous function ($f(x) = x$) then the resulting function is still continuous.
Not differentiable:
We are only allowed to take the differential quotient in some neighborhood of a limit point of the domain of the function. Since the domain of our sequence has no limit points, it cannot be differentiable.
Do you think that my explanation is satisfactory?