{"id":18366579,"url":"https://github.com/ajcr/transfinite","last_synced_at":"2025-06-13T11:09:21.809Z","repository":{"id":78934830,"uuid":"43846084","full_name":"ajcr/transfinite","owner":"ajcr","description":"Transfinite ordinal arithmetic and factorisation up to epsilon-zero","archived":false,"fork":false,"pushed_at":"2022-03-22T22:00:09.000Z","size":460,"stargazers_count":14,"open_issues_count":1,"forks_count":1,"subscribers_count":4,"default_branch":"master","last_synced_at":"2025-05-28T04:06:27.425Z","etag":null,"topics":["arithmetic","factorization","ordinals","python","set-theory","transfinite"],"latest_commit_sha":null,"homepage":"","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ajcr.png","metadata":{"files":{"readme":"README.md","changelog":"changelog.md","contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2015-10-07T21:36:07.000Z","updated_at":"2024-10-31T09:58:46.000Z","dependencies_parsed_at":null,"dependency_job_id":"8e674c56-5189-46a7-8572-847d539800cf","html_url":"https://github.com/ajcr/transfinite","commit_stats":{"total_commits":96,"total_committers":2,"mean_commits":48.0,"dds":0.01041666666666663,"last_synced_commit":"5513c23531b0140bee0aa5f9be7a67cea2d959ea"},"previous_names":[],"tags_count":6,"template":false,"template_full_name":null,"purl":"pkg:github/ajcr/transfinite","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ajcr%2Ftransfinite","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ajcr%2Ftransfinite/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ajcr%2Ftransfinite/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ajcr%2Ftransfinite/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ajcr","download_url":"https://codeload.github.com/ajcr/transfinite/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ajcr%2Ftransfinite/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":259634382,"owners_count":22887700,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["arithmetic","factorization","ordinals","python","set-theory","transfinite"],"created_at":"2024-11-05T23:18:20.298Z","updated_at":"2025-06-13T11:09:21.782Z","avatar_url":"https://github.com/ajcr.png","language":"Python","readme":"# transfinite\n\n[![PyPI version](https://badge.fury.io/py/transfinite.svg)](https://badge.fury.io/py/transfinite)\n\nTransfinite [ordinal arithmetic](https://en.wikipedia.org/wiki/Ordinal_arithmetic) and factorisation up to the first [epsilon number](https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)).\n\n## Installation\n\nWorks with Python 3. Can be installed via pip using:\n\n```\npip install transfinite\n```\n\n## Usage\n\nFor a basic introduction to ordinal arithmetic, look at Wikipedia or see the notebook [here](https://github.com/ajcr/transfinite/blob/master/notebooks/ordinal_arithmetic_basics.ipynb).\n\nHere's a quick demonstration of the library in Jupyter's qtconsole (note that the variable `w` is the first transfinite number). First, some ordinal arithmetic:\n\n![alt tag](https://github.com/ajcr/transfinite/blob/master/images/transfinite_demo.png)\n\nThe Ordinal class implements several methods which can be used to check properties of the ordinal:\n\n- `Ordinal.is_limit()`, returns True if the ordinal is a [limit ordinal](https://en.wikipedia.org/wiki/Limit_ordinal).\n- `Ordinal.is_successor()`, returns True if the ordinal is a [successor ordinal](https://en.wikipedia.org/wiki/Successor_ordinal).\n- `Ordinal.is_gamma()`, returns True if the ordinal is [additively indecomposable](https://en.wikipedia.org/wiki/Additively_indecomposable_ordinal).\n- `Ordinal.is_delta()`, returns True if the ordinal is [multiplicatively indecomposable](https://en.wikipedia.org/wiki/Additively_indecomposable_ordinal#Multiplicatively_indecomposable).\n- `Ordinal.is_prime()`, returns True if the ordinal is prime.\n\n[Ordinal factorisation](https://en.wikipedia.org/wiki/Ordinal_arithmetic#Factorization_into_primes) into prime ordinals is also implemented. Any composite ordinal `a` can be written as a product of two or more prime ordinals less than `a`:\n\n![alt tag](https://github.com/ajcr/transfinite/blob/master/images/transfinite_demo_2.png)\n\nNote that finite ordinals are not factorised using this method.\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fajcr%2Ftransfinite","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fajcr%2Ftransfinite","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fajcr%2Ftransfinite/lists"}