Comment
Your definition is good, but it might be a little clearer if you used $ t_0 $ rather than $ t $ so as to emphasize a particular moment in time. - Jacob Pfister
The defination is clear to me, but a good example would help to clear away any doubts that anyone have. - Wei Jian Chan
Your definition is reasonable, but you almost seem to contradict yourself at times. I agree that using a separate variable such as $ t_0 $ would make it much clearer.
