# I Understanding the Dirac Delta function

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1. May 28, 2017

### redtree

I just want to make sure that I am understanding the Dirac Delta function properly. Is the following correct?:

For two variables $x$ and $y$:

\begin{split}
\delta(x-y) f(x) &= f(y)
\end{split}

And:

\begin{split}
\delta(x-x) f(x) &= f(x)
\end{split}

2. May 28, 2017

Staff Emeritus
Neither of those is correct.

3. May 29, 2017

### Ssnow

The Dirac delta is not a function in the traditional sense, it can be rigorously defined either as a distribution or as a measure.
Ssnow

4. Jun 8, 2017

### FactChecker

The Dirac delta function is defined as a generalized function by its behavior in an integral: ∫f(x)δ(x)dx = f(0).
So in your question, ∫δ(x-y)f(x)dx = f(y) would make better sense than your expression (1). The integral can not be omitted. Your expression (2) does not make sense to me.