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This math, or just looking at your TV, tells you that you can't see individual pixels. What's interesting is that a 720p, 50-inch TV has pixels roughly 0.034 inch wide. As in, at a distance of 10 feet, even 720p TVs have pixels too small for your eye to see.
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I think if you are watching a 50" TV from 10' away, you are sitting too far back. I'm not advocating 4K but screen size and distance from the screen is what I look at when buying a TV, so 4K could be a reasonable choice. Myself I watch my 55" 1080p from about 7.5' and I could probably go up to 60" or even 65" to get the best experience. People just coming into HD often make the mistake of getting too small of a TV because they grew up with a SD 27" at 10' away.