Actually the Sun never sets on a flat earth because instead of going around the Earth like a hula hoop, instead it circles the perimeter of the flat Earth like a halo. This is somewhat problematic because when you think about it, that arrangement would never allow for darkness because the Sun would be shinning everywhere all the time-- brighter in some spots while dimmer in others but none would be dark.
It does not circle "the perimeter of the flat Earth" - it circles above the earth between the 'tropic' lines.
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If you suggest that the light of the sun would be "brighter in some spots while dimmer in others"...
1)
What exactly is it that would cause this to be - as opposed to the same amount of light everywhere?
2) Why do you not believe that there could be enough of [#1 answer] to cause complete darkness if the sun was far enough away?
Why would you believe that the light of the sun was "continually more dim" with distance yet could always be seen at an 'infinite' distance?
The answer to the first question is [the] 'atmosphere'. More particularly - the moisture, dust, smoke, etc. that is in the 'atmosphere'.
If you get far enough away from a flashlight - it will no longer be seen. Same thing. No difference.
The sun does not have 'infinite' brightness. The light of the sun is
diminished by the 'atmosphere'.
With a sufficient amount of 'atmosphere' between you and the sun - you will not be able to see its light.
You should also keep in mind that, in the Flat Earth model, the sun is not "a thousand times
larger" than the earth - it is "a thousand times
smaller" than the earth. (It might help you to "visualize" it better.)