I am just learning some higher level mathematics, and there is a continuous emphasis on definitions and theorems, which ultimately form the foundation of proofs.
I am trying to look at what sort of information should go into a formal definition.
For example, i came across the formal definition of a composite number:
'A natural number $n \in \mathbb{N} $ is called a composite number if $n \neq1$ and there exist $a, b\in \mathbb{N} $ with $1 \lt a, b\lt n$ such that $n=ab$.'
This captures the notion of a composite very precisely, but I'm not sure why you would want to explicitly state '$n\neq1$', as, if $n$ is composed of $a, b \gt 1$, then surely it is obvious that $n\neq 1$?