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A lowercase delta of a variable, infinitely tall and infinitely narrow.
Also known as: Unit impulse, Delta function, Impulse function, Dirac delta
The Dirac delta is not a function: it is zero everywhere except at one point and integrates to one, which no function does. It is defined by what it does inside an integral — it picks out the value of whatever it multiplies at that point — and that is the only definition that survives scrutiny.
Denotes the Dirac delta distribution: zero away from the origin, with unit integral, defined by its sifting action inside an integral.
Contexts: Mathematics
Is not a function in the ordinary sense; it is a distribution, and treating it as a function produces contradictions.
Contexts: Mathematics
Was introduced by Paul Dirac in quantum mechanics and given rigorous footing later by Laurent Schwartz's theory of distributions.
Contexts: Mathematics
A lowercase Greek delta followed by a bracketed variable, drawn in illustrations as a single upright arrow of unit height.