The dots that shine on a CRT don’t correspond 1:1 to the pixels, or even the scan lines, of the image sent to it. The shadow mask has tiny holes that keep the three electron beams from hitting the wrong colors, but a single scan line is usually a few dots thick and with faded edges. This makes them look a lot softer and less pixelated than the hard-edged pixels of an LCD raster.
Edit: here’s an image, where you can see how very soft the shapes become: https://live.staticflickr.com/3358/3563978211_21b9e5e1fd_b.jpg
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