Does there exist a bijection between empty sets? 
Does there exist a bijection between empty sets?

What I think is:
Since 'for every $x\in \emptyset$, there exists $y\in \emptyset$ such that $(x,y)\in f$' is false and the negation of this statement is also false because of 'existence' sentence..  
But I think empty sets are equipotent intuitively.
Am I wrong? Help

Note that there are not "empty sets", because the axiom of extensionality tells us that all empty sets are equal, as they have the same elements.
Now it is obvious that there is a bijection of a set to itself. The identity, furthermore if you think of it a little bit you will see that the empty set itself is a function whose domain and range are empty, and therefore it is a bijection between that set and itself.
Further reading:


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*Why is an empty function considered a function?
