The Dirac delta can be loosely thought of as a function on the real line which is zero everywhere except at the origin, where it is infinite,
and which is also constrained to satisfy the identity
This is merely a heuristic characterization. The Dirac delta is not a function in the traditional sense as no function defined on the real numbers has these properties. The Dirac delta function can be rigorously defined either as a distribution or as a measure.
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