AirPlay to TV without using monitor
I have a new AppleTV and am trying to figure out how to set it up, much in the same way as an external monitor that allows me to close the MBAir and continue operations. Is it possible to not have the computer open and displaying the same material that is being sent to the television? Thus far I can't wrap my head around why this doesn't seem easy to do. And, if it's not possible, what am I not grasping about the utility of this device? Thus far, the AppleTV seems to have the same functionality that can be achieved using a bluetooth keyboard/mouse and a thunderbolt cable...đ