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

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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.
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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Date/TimeThumbnailDimensionsUserComment
current15:20, 1 June 2024Thumbnail for version as of 15:20, 1 June 20241,017 × 1,446 (205 KB)Watchduck (talk | contribs)details
07:42, 7 August 2014Thumbnail for version as of 07:42, 7 August 20141,052 × 1,488 (204 KB)Wereldburger758 (talk | contribs)Saved 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)Watchduck (talk | contribs)reupload, 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 (talk | contribs)
13:33, 10 May 2009Thumbnail for version as of 13:33, 10 May 2009744 × 984 (122 KB)Watchduck (talk | contribs){{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

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