Careful, resolution independence isn't a magic solution. Your post makes sense if the 46" widescreen TV is a high-resolution one (1080p for example) but many LCD TV's offer much poorer resolutions than computer monitors. Resolution indepedence makes most sense for high-resolution LCD screens that pack a lot more pixels in (like the Dell laptop I once had, that crammed 1920x1080 pixels into a 15" display).
Resolution independence means that the OS dynamically scales things instead of always mapping them pixel-by-pixel. For example, how tall is the standard OS X menu bar? I don't have one handy but let's say it's 30 pixels tall. 30 pixels on a 15" LCD running 1024x768 looks a lot different from 30 pixels on a 30" LCD running 2560x1600.
A resolution independent OS would say that the menu bar should be, say, 1/4" tall, and scale the number of pixels and font sizes accordingly. Maybe it's 30 pixels on a 15" LCD, but 65 pixels on a huge 30" monitor, or maybe 22 pixels on the bigscreen TV.