# Talk:Real Function is Continuous at Point iff Oscillation is Zero

The problem I have with this:

$\forall I: x \in I, \omega_f \left({I} \right) \ge \epsilon$

is that it offers a proposition with two bound variables an expression with only one of those variables.

As an expression in pure predicate logic, it would be written:

$\forall a: \forall b: P \left({a}\right)$

The proposition is in $a$, and in that proposition there is no mention of $b$. So what is the purpose of $b$ in that proposition? --prime mover (talk) 18:29, 9 December 2015 (UTC)

NO -- you're all right, I understand now! I take it to mean:
For all real intervals that have $x$ in them, the oscillation is greater than $\epsilon$.
It's the comma that confuses me. There is only one use for a comma in mathematics, and that is to separate elements of lists. So often it's used to mean "such that", which is suboptimal. --prime mover (talk) 20:14, 9 December 2015 (UTC)