 We can reconstruct large parts of the mathematical universe by selecting appropriate mathematical example objects to populate it, beginning with the assumption that there is a single unique empty set \(\emptyset\) which represents the number 0. This gives us the existence of a set with only one member \(\{\varnothing\}\) to represent the number 1 and repeating this construction, \(\{\varnothing,\{\varnothing\}\}\) for 2, the whole set of natural numbers \(\mathbb{N}\) emerges. Elementary arithmetic then is defined on the basis of Peano’s axioms:  