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[Phys-l] zero width?



Ben Wittner tells this story:


When he was in primary school, the teacher said:
"Everything has some size. In mathematics, they say a line has
zero width, but I don't believe it. If I draw a line with this
chalk, it has some width. If it didn't have any width, it wouldn't
exist."

At this point Ben pipes up:
"I can draw something with zero width."

The teacher said:
"Show me."

So Ben went up to the chalkboard and ......

So the puzzle is: What happened next?

The answers I'm looking for might take the form:
-- If you think it is not possible to draw something with zero
width, explain why not.
-- If you think it is possible, explain the best way to go about it.