Math and science::Analysis::Tao::10: Differentiation of functions

# Differentiability on a domain

Let \( X \) be a subset of \( \mathbb{R} \) and let
\( f : X \to \mathbb{R} \) be a function. We say that \( f \) is differentiable
*on \( X \)* iff for every limit point \( x_0 \in X \), \( f \) is
differentiable at \( x_0 \) on \( X \).

Tao describes this as an *if* rather than
*iff* statement.

I think this definition is allowing isolated points to be ignored. Note how the limit point is also an element, so we are also excluding points that are limit points but not in the \( X \).