is this standard notation $\mathcal{N}=\{1,\ldots,n|\;n>2\}$?

I am more interested to know if we use $|$ vertical lines in set notation to specify a certain condition that characterizes the set.

@johnny09 it is not standard notation. The standard notation is $\{x\in A\mid \mbox{condition}\}

Okay, thanks!

do you know when do we use $:$ in sets?

eg $A=\{a : a>0\}$

Would it make more sense if I write $\mathcal{N}=\{1,\ldots,n : n>2\}$?

@johnny09 : and | are the same, the problem is 1,...,n is not well defined

@johnny09L the second one, \{1,\ldots,n : n>2\}, doesn't make sense. That says "the set of 1, 2, ..., n where n > 2". What set are you trying to define?

There are two general ways to use the notation correctly. If you write { n in N : n > 2 } this means "the set of n in N so that n > 2". If you write { m + 2 : m in M } you mean "the set of all numbers that can be written int he form m + 2 where m in N". There are many more examples at en.wikipedia.org/wiki/Set-builder_notation

thanks for the answers everybody!

just for verification: suppose we have the set $S=\{x\in\mathbb{R} | 1<x<3,x=4\}$

the interior set of S is $(1,3)$, the isolated point is $x=4$, the closure is $\{x\in[1,3],x=4\}$

the accumulation points or limit points are any $x\in[1,3]$

$S$ is neither open nor closed as $S=\{x=4\}\cup(1,3)$ and $(1,3)$ is open but $x=4$ has no interior and so it is closed

i am not sure but is the boundary of $S$ the three points $x=1,x=3,x=4$?