  Although we'll say more about this kind of issue later (see especially sections  2.1  and  3.1), a few preliminary remarks are appropriate here. First, it's important to note that there are some set-theoretic concepts which first-order models do capture quite precisely. As we'll see in section 3.1, first-order models capture finite cardinality notions—e.g., “x is empty,” “x has two members,” “x has seventeen members,” etc.—quite nicely.[9]  If we allow ourselves to use infinitely many formulas, then we can also capture the more-general notion “x is  infinite.”[10]  Finally, if we fix our understanding of membership—i.e., if we restrict our attention to models which use the real membership relation to interpret the symbol “∈”—then we can also capture the general notion “x is  finite.”[11]