Construct the natural numbers with sets
Python, 28 bytes



lambda x:"{{}"*x+x*"}"or"{}"


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This is a pretty bland solution to the problem.  For numbers greater than zero you can get the representation with the string formula "{{}"*x+"}"*x.  However this doesn't work for zero where this is the empty string.  We can use this fact to short circuit an or to return the empty set.

I wanted to use python's builtin set objects to solve this problem but unfortunately:

TypeError: unhashable type: 'set'


You cannot put sets inside of sets in python.