 From the principle of microaffineness it also follows that all functions on \(\bR\) are continuous, that is, send neighboring points to neighboring points. Here two points \(x, y\) on \(\bR\) are said to be neighbors if \(x - y\) is in \(\Delta\), that is, if \(x\) and \(y\) differ by a microquantity. To see this, given \(f: \bR \rightarrow \bR\) and neighboring points \(x, y\), note that \(y = x + \varepsilon\) with \(\varepsilon\) in \(\Delta\), so that