Please explain the relation between bandwidth and gain of op-amp.
I have learned that negative feedback could reduce gain and increase bandwidth of an amplifier. Since gain= Vout/Vin, I understand that less gain means higher Vin. The larger Vin, the greater bandwidth. (I made my own assumption here. Please correct me if I am wrong!)
However, this seemed contradictory with what I knew about the properties of an ideal operational amplifier (op-amp). The ideal op-amp should has infinite open-loop voltage gain and infinite bandwidth. How can infinite open-loop voltage gain has infinite bandwidth? Or this is why it is an ideal op-amp (impossible to be made).
This confuses me a lot. Thank you for your help!