I have seen a singleton in the [0,1] set defined as:
$\{b\}=\bigcap\limits_{n=1}^{\infty}(b-1/n, b+1/n] \,\cap\,\Omega$
I am trying to learn some set theory in connection to the need for probability spaces, and their relation to $pdf$'s. Specifically, I'm having problems understanding the idea of a singleton.
I have two questions: The main one is how unequivocal the $\infty$ symbol is in the definition? In other words, isn't the cardinality of $\infty$ a loose end in that definition of singleton in the way expressed above? Sort of including the defined in the definition?
And a probably lesser relevant issue: why the open left parenthesis when the expression is closed with a bracket on the right?