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Topic: dirac delta function is not a TRUE function??
Replies: 11   Last Post: Jul 19, 2011 11:08 PM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: dirac delta function is not a TRUE function??
Posted: Jul 12, 2011 3:46 AM
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> Hi all,
> From WIKI, I learn that dirac delta function is not a true function.
> However, I do not understand the explanation in WIKI and still get
> confused, why it is not a TRUE function.

There is no function delta, in the usual sense of the word function,
such that

delta(x) = 0 if x =/= 0


int_-infty^+infty delta(x) dx = 1

> Could you please help me to understand it?

It may be understood as a distribution, see

When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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