I haven't learned first-order logic in a systematic way.
Question. What is the correct way to write in first-order formulas correctly the following statement?
For any natural number $n$, $P(n)$ is true.
Two candidate I come up with are the following:
- $\forall n$ $(n\in{\bf N}\to P(n))$
- $\forall (n\in{\bf N})P(n)$
The second one can not be right according to the instruction in this Wikipedia article. However, it is also used in another article.