Prove that (n) = u(n)-u(n-1)

Prove that (n) = u(n)-u(n-1)

    We know that u(n) = 1 for n ≥ 0 , 0 for n < 0 and u(n-1) = 1 for n ≥ 0 , 0 for n < 1 

Hence, u (n)-u (n-1) = 0 for n≥1 i.e., n>0 

    1 for n=0 

    0 for n<0 

The above equation is nothing but δ(n).i.e., 

u(n)-u(n-1) = δ(n)=1 for n=0 = 0 for n≠0