 What are the algebraic and order structures on \(\bR\) in SIA? As far as the former is concerned, there is little difference from the classical situation: in SIA \(\bR\) is equipped with the usual addition and multiplication operations under which it is a field. In particular, \(\bR\) satisfies the condition that each \(x \ne 0\) has a multiplicative inverse. Notice, however, that since in SIA no microquantity (apart from 0 itself) is provably \(\ne 0\), microquantities are not required to have multiplicative inverses (a requirement which would lead to inconsistency). From a strictly algebraic standpoint, \(\bR\) in SIA differs from its classical counterpart only in being required to satisfy the principle of infinitesimal cancellation.