A mathematical interpretation of Dirac's \(\delta\) function (Q1086788)

The two conditions \[ (1)\quad \delta (x)=0,\quad for\quad x\neq 0,\quad (2)\quad \int^{+\infty}_{-\infty}\delta (x)dx=1 \] of the Dirac \(\delta\) function are inconsistent in standard analysis. In this paper, the author began by studying the integral of the functions on the nucleon \(\alpha\) (0), and then, making use of the point function in infinitesima analysis to define the Dirac \(\delta\) function \(\delta\) (x) so that it satisfies the condition (2) and \(\delta (x)=0\), for \(x\in R\) and \(x\neq 0.\) Some various examples of Dirac \(\delta\) functions have been presented and some properties of the \(\delta\) function have been derived.