 For hyperreals \(a, b\) we define \(a \approx b\) and say that \(a\) and \(b\) are infinitesimally close if \(a - b \in I\). This is an equivalence relation on the hyperreal line: for each hyperreal \(a\) we write \(\mu(a)\) for the equivalence class of \(a\) under this relation and call it the monad of \(a\). The monad of a hyperreal \(a\) thus consists of all the hyperreals that are infinitesimally close to \(a\): it may be thought of as a small cloud centered at \(a\). Note also that \(\mu\)(0) \(= I\).