There's a difference between f(0) and lim t->0 f(t). We just chose to treat this function as a "staircase function" where f(0) =lim t->0 f(t), general formula

There's a difference between f(0) and lim t->0 f(t). We just chose to treat this function as a "staircase function" where f(0) =lim t->0 f(t), general formula for f(t!=0).