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

Thanks you in advance

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The definition of the singularity function $ <x-a>^0 $ is 0 if $x<a$ 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.

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