Delta type function

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I am looking for a function, $f(x)$ that is equal to 1 if $x=a$ and $0$ for any other value. Initially, I thought of delta function, but this equals $\infty$ at $x=a$. Any idea on what this could be?

Thanks!

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This is the Indicator Function for the set $\{a\} \in \Bbb{R}$.