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Looking for some discussion on a What are possible resolutions of the length unit paradox stemming from Zeno's Paradoxes?

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Looking for some discussion on a paradox stemming from Zeno's Paradoxes

The paradox in question: If every unit of length is made up of smaller units of length, it seems that you need to have units of length before a unit of length can come into existence. But this is clearly contradictory.

This paradox would seem to imply the following. Say you have two lines lying exactly on top of one another "|", and you want to slide one off the other to create space between the two, so that it now looks like this "||". If we need units of length before a unit of length can exist, then it seems we cannot create a length of distance between these two lines when we started with none, as we would need to have some length of distance already between them before we could have any length of distance between them.

Where does this reasoning go wrong?