Definition of the Number Two in ZF Set Theory

Question

This page shows how natural numbers may be defined as unions of sets.

What is a straightforward way to appeal to intuitive notions to dispel the misconception that
{Ø} + {Ø} = {{Ø}, {Ø}, Ø} and instead show that
{Ø} + {Ø} = {Ø, {Ø}}
?

Answer 1

Note that $\{x,x,y\}=\{x,y\}$. So the two sets you suggest are in fact the same.