pyZFC 0.2.0

(ZFC) set-theoretic definition of natural numbers.

ZFC: set-theoretic definition of natural numbers in Python

Installation

pip install pyZFC

Introduction and examples

NaturalNumber is the class of natural numbers defined as von Neumann ordinals in the ZFC set theory.

0 is defined as the empty set {}, and the rest of the natural numbers are defined recursively as n + 1 = n ∪ {n}, i.e.,

0 = {},
1 = {0},
2 = {0, 1},
3 = {0, 1, 2},
...

Following the definition, you can do all kinds of set operations on natural numbers, e.g., checking whether a NaturalNumber contains another.

>>> from zfc import NaturalNumber

>>> NaturalNumber(1) in NaturalNumber(2)
True

>>> NaturalNumber(1) & NaturalNumber(2)
1  # the intersection of 1={0} and 2={0,1} is {0}, which is exactly 1.