Hi all! Can anyone explain me why " a power series is asymptotic to a function" is defined as shown in the picture? Referring to the first definitoin, it means that the remainder after N terms should be much smaller than (x-xo)^N? Actually, I can't "sense" the meaning of such definition. Maybe, sometimes, a definition may not bare any meaning.... But, "asymptotic", in my mind, means "closer and closer" to something. And I guess this defintion should bare some implication for this. Can anyone explain this defintion for me? I am completely stucked with this..Please kindly help.