 If \(A\) is a standard set, we may consider the collection \(\hat{A}\)—the inflate of \(A\)—consisting of all the *-members of \(A\): this is not necessarily a set nor even a *-set. The inflate \(\hat{A}\) of a standard set \(A\) may be regarded as the same set \(A\) viewed from a nonstandard vantage point. While clearly \(A \subseteq \hat{A}\), \(\hat{A}\) may contain “nonstandard” elements not in \(A\). It can in fact be shown that infinite standard sets always get “inflated” in this way. Using the transfer principle, any function \(f\) between standard sets automatically extends to a function—also written \(f\)—between their inflates.