$2\delta(x) \neq \delta(x)$ since, by definition,
Can this been seen graphically though?
If so, how?
If not, why is it that they are mathematically different but graphically the same?
Btw, I don't understand any precise definitions here so please dumb down your answers to the level of someone who knows basic Real Analysis and Partial Differential Equations, and just pretend I don't really know what the Dirac Delta function is. Thanks.
Context: I thought the derivative of the sgn function was the Dirac Delta Function(al)/Distribution when it is really twice of it (http://en.wikipedia.org/wiki/Signum_function#cite_ref-2). I was thinking they would turn out to to be equal. Is it really wrong to say that the derivative of the sgn function is the Dirac Delta Function(al)/Distribution? I just can't visualize this.