 Dirac is of course fully aware that the \(\delta\) function is not a well-defined expression. But he is not troubled by this for two reasons. First, as long as one follows the rules governing the \(\delta\) function (such as using the \(\delta\) function only under an integral sign, meaning in part not asking the value of a \(\delta\) function at a given point), then no inconsistencies will arise. Second, the \(\delta\) function can be eliminated, meaning that it can be replaced with a well-defined mathematical expression. However, the drawback in that case is, according to Dirac, that the substitution leads to a more cumbersome expression that obscures the argument. In short, when pragmatics and rigor lead to the same conclusion, pragmatics trumps rigor due to the resulting simplicity, efficiency, and increase in understanding.