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We have described the sets above by listing their elements. Sometimes this is hard to do, especially when there are a lot of elements in the set (perhaps infinitely many). For instance, if we want \(A\) to be the set of all even natural numbers, would could write,

\begin{equation*} A = \{0, 2, 4, 6, \ldots\}\text{,} \end{equation*}

but this is a little imprecise. A better way would be

\begin{equation*} A = \{x \in \N \st \exists n\in \N ( x = 2 n)\}\text{.} \end{equation*}

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