Jump to content

File:Nested set V4; elements in Hasse diagram.svg

Page contents not supported in other languages.
From Wikiquote

Original file (SVG file, nominally 1,017 × 1,446 pixels, file size: 205 KB)

This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.

Summary

Description
The subsets of V_4 are numbered in reverse binary order.
The subsets of V_4 are numbered in reverse binary order.

The elements of V4 - respectively the subsets of V3 - ordered in a Hasse diagram by inclusion.

V4 = P^4({}) = P( P( P(P({})))) is the powerset of the power set of the power set of the power set of the empty set.

As many brackets are usually hard to understand, the sets are defined by circles instead of brackets. The circle containing nothing stands for the empty set.

The universe (the thing all shown sets are a subset from) in this Hasse diagram is P^3({}) and expressed in set brackets it looks like this:

{ {} , {{}} , {{{}}} , {{},{{}}} }

This system of sets can be used for a set theoretic definition of Boolean functions.
Date
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions

Printable version: File:Nested set V4; elements in Hasse diagram.pdf

Compare:
SVG development
InfoField
 
The SVG code is valid.
 
This diagram was created with Inkscape, or with something else.

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

10 May 2009

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:20, 1 June 2024Thumbnail for version as of 15:20, 1 June 20241,017 × 1,446 (205 KB)Watchduckdetails
07:42, 7 August 2014Thumbnail for version as of 07:42, 7 August 20141,052 × 1,488 (204 KB)Wereldburger758Saved as plain SVG. Valid SVG now.
21:28, 27 May 2010Thumbnail for version as of 21:28, 27 May 20101,052 × 1,488 (297 KB)Watchduckreupload, to make the file actually shown
14:13, 13 June 2009Thumbnail for version as of 14:13, 13 June 20091,052 × 1,488 (343 KB)Watchduck
13:33, 10 May 2009Thumbnail for version as of 13:33, 10 May 2009744 × 984 (122 KB)Watchduck{{Information |Description={{en|1=...}} {{de|1=...}} |Source=Eigenes Werk (own work) |Author=Lipedia |Date=2009-May-10 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> Category:Hasse diagrams

Global file usage

The following other wikis use this file:

Metadata