 We shall call a quantity having the property that its square is zero a nilsquare infinitesimal or simply a microquantity. In SIA “enough” microquantities are present to ensure that equation (2) holds nontrivially for arbitrary functions \(f: \bR \rightarrow \bR\). (Of course (2) holds trivially in standard mathematical analysis because there 0 is the sole microquantity in this sense.) The meaning of the term “nontrivial” here may be explicated in following way. If we replace \(\delta x\) by the letter \(\varepsilon\) standing for an arbitrary microquantity, (2) assumes the form