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That's the highest resolution it can display on the laptop screen, 1080 can be displayed on an external monitor/HDTV via HDMI cable. 1600x900 resolution on a 14" laptop screen is a very high quality though, far exceeding the amount of pixels per square inch of a large screen 1080p TV screen.
As long as the screen is capable of and set for 1920X1080 (thats the size of 1080p HD) or higher
Blurry
Your HDTV can only play 1080 p when the material is 1080P
1920x1080
Most Mac monitors run on 1080p.
yes
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As far as I know HDMI does have some form of support for 4K, but don't expect eery piece of hardware to be run perfectly with such (if anything, the setup you describe will probably be bottlenecked at 1080p if it doesn't complain about resolution formats).
The main advantage of a laptop with a HDMI output is that you will be able to display video at a full 1080p resolution. Cable simplification would be another advantage, because HDMI can carry both audio and video.
I use a 47" and I love it. I'll never go back to my 24 :)
1080p