# Singularity function

Could you please tell me why the singularity function is one when x=0 I mean $$<0> ^0=1$$

Thanks you in advance

The definition of the singularity function $$^0$$ is 0 if $$x and equal to 1 if $$x\ge a$$. It does not matter if x-a is 0 or infinity; the value is still 1.
Therefore, $$<0>^0 = 1$$ by definition.