eset

Extended sets - support for set complement

Overview

An eset works like a normal python set except that you can invert it to generate its complement. For example, let's say you have the following:

>>> from esets import eset
>>> s = eset(['hello', 'there'])
>>> s_invert = ~s
>>> s_invert
~eset(['hello', 'there'])

In this example, s_invert contains everything except 'hello' and 'there'.

Logic

All the logic operations you'd expect from sets are available in esets, including intersection, union, difference, and symmetric difference. Use the &, |, -, and ^ operators respectively.

Similarly, conditional expressions are available to determine subset relationships. If A <= B, that A is a subset of B.

Infinities

You'll note there's an inf.py module that implement א‎0 and א‎1 infinities, that is, countable and uncountable infinities. This was implemented so that cardinality calculations would be correct for complement sets: discussed below.

>>> from esets import inf
>>> inf.countable, inf.uncountable
(א‎0, א‎1)
>>> inf.countable < inf.uncountable
True

Cardinality

The abs expression (also cardinality method) will return a countably infinite scalar if in complement mode; otherwise it returns the count of items in set.

>>> from esets import eset, inf
>>> s = eset(['hello', 'there'])
>>> abs(s)
2
>>> abs(~s)
א‎0