The statement "For all $x$ in the set of natural numbers ($N$), $x > 0$" can be written as an English sentence like this:

"For every $x$ that is a natural number, $x$ is greater than 0."

This statement is true, as natural numbers ($N$) are typically defined as the set $\{1, 2, 3, \dots \}$, which excludes 0. Therefore, all natural numbers are indeed greater than 0.

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. What is the formal definition of the set of natural numbers?
2. How does the set of whole numbers differ from the set of natural numbers?
3. What are some other common sets of numbers, like integers or real numbers?
4. What is the symbol ∀, and how is it used in mathematical logic?
5. Can natural numbers include 0 in some definitions?

Tip: Always clarify whether your definition of natural numbers includes 0, as it varies depending on the context!