I am currently working on the famous "locker problem." For those unfamiliar with this problem, this question here does a great job of explaining what it's all about.
My question today has to do entirely with the bottom of pg. 2 of this document. The author makes the following definition
"Given a set $A$ of natural numbers, let $e(A)$ be all natural numbers that are greater than or equal to an even number (including $0$) of the elements of $A$."
to which he offers the following example
"For example, if $A = \{3, 6, 9, . . .\}$, then $e(A) = \{1, 2, 6, 7, 8, 12, 13, 14, 18, 19, 20, . . .\} = \{n ∈ N : n ≡ 0, 1, 2 \mod 6\}$."
I do not understand what this function $e(A)$ is doing. Perhaps the wording of his definition is awkward and is causing my confusion. Do any of you know what he is saying here?
$e(A)$ is the set of all positive integers $n$ such that the cardinality of the set $A\cap \{1,2,\dots,n\}$ is even.