Also, is there a way to set the badge to 0 while keeping the notifications in the notification center if the application has a badge and there are notifications in the notification center?

Is my understanding correct that if the application has a badge and there are notifications in the notification center, calling application.applicationIconBadgeNumber = 0 will clear all notifications in the notification center, but if the application does not have a badge and there are notifications in the notification center, calling application.applicationIconBadgeNumber = 0 will not clear the notifications in the notification center?