I want to know how to write: '$n$ is a natural number bigger or equal to two' in mathematical terms. My thoughts:
- $$n\in\mathbb{N} \setminus \{0,1\}\tag1$$
- $$n\in\mathbb{N}_{\ge2}\tag2$$
- $$ n\in\mathbb{N}\space\wedge\space n\ge2\tag3$$
Which one is the best? Or am I wrong about this.
Best Answer
Writing mathematically an expression doesn't mean you have to use only symbols. Often, for clarity is better to combine symbols and words.
Also writing with only symbols tends to be more prone error.
It's better to say
"Any non-empty subset of natural numbers has a minimum"
or
"For any $A \subseteq \mathbb N$, if $A\ne\emptyset$ then there exists a minimum element $a\in A$"
that
$\forall A (A\subseteq \mathbb N \,\wedge A\ne\emptyset \implies \exists a(a\in A\, \wedge\forall b(b\in A \implies a\le b)))$
For the specific statement you are asking i would use something like "Let $n\in \mathbb N, n\ge 2$".
Actually, often $n$ denotes a natural number, so, unless the context could lead to confusions, i would only write "Let $n\ge 2$".