I think I am missing something when trying to understand the meaning of ROC curve. More specifically, I don't understand why a square with AUC of 1 (100% of the area) is considered ideal. This implies that a classifier results range from achieving TPR/FPR of 1/0 to 1/1 for various thresholds. Yet, isn't the ideal situation 1/0 for any threshold value? That implies no curve is constructed and AUC is undefined.
I am probably understanding something fundamentally wrong.