There is no definite moment when a day ends and tomorrow begins, nor is there a definite moment when yesterday ended. Time is not a discrete variable.
Consider the concept of the present. There is no definite moment when it ends and the future begins, nor is there a definite moment when the past ended and the present begun. In fact, the concept of time itself seems to be an illusion. Whatever we hold memories of we call past. Whatever we know nothing of we call future. And present is kind of both past and future, which is expected of a continuous variable. The left-had limit (past) and the right-hand limit (future) at present must be the same. Are they?
The mathematics here suggests that past, present, and future are not three discrete functions but one continuous one. Is there time if no one is watching? Is it time that changes/passes? Is it we who change? Or is it we who feel like we change?
Perhaps, it is a result of egotistical perception. The self is a localized occurrence. People localize themselves to a point they call present. Whatever they have memories of they call past. Whatever they are uncertain about they call future.