The Dirac Delta can be seen as a continuous generalization of the Kronecker Deltapic.twitter.com/wnJDykOglK
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I struggle to accept it is used like a function.
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Actually, I think the way it was presented to me in class and books was lacking rigour. If it's not a function, but a limit of a functional distribution, how can it be used with a "normal" function in an integral and have this "filtration" property. And another question...
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...Why is it's integral over all space 1? And how can it be, that, for example, if I have a rope with homogeneous density(p_0), and a mass m at some point of if, we can model the mass density as a function of space with p(x)=p_0+m*delta?
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