TITLE: Is the Dirac Delta "Function" really a function?
QUESTION [36 upvotes]: I am given to understand that the Dirac delta function is strictly not a function in the conventional sense and it is a "functional or a distribution".
The part which I can not understand why the Delta "function" makes sense only when it acts on another function and that too only inside an integral and how is a "functional" or "distribution" different from a function.

REPLY [6 votes]: $\delta$ is a function to exactly the same extent that $\infty$ is a number.