Answer:
Considering this from a physics point of view, age or the progression of time d*/dt is continuous. I know I am continuously aging. Of course when we speak of our age we tend to jump and ignore fractional changes right? One day we're 28 and stay that way for 364 days, then bang we're 29. No one says well I'm 28.6 years old. Some seem to be stuck at 29, until they have to be honest about it and there is an abrupt change to say 40.