 A hyperreal \(a\) is finite if it is not infinite; this means that \(\lvert a\rvert \lt n\) for some \(n \in \bbN\) . It is not difficult to show that finiteness is equivalent to the condition of near-standardness; here a hyperreal \(a\) is near-standard if \(a \approx r\) for some standard real \(r\).