Proper class: Difference between revisions
Jump to navigation
Jump to search
Content added Content deleted
Cobsonwabag (talk | contribs) No edit summary |
CreeperBomb (talk | contribs) (Undo revision 687 by Cobsonwabag (talk)) Tag: Undo |
||
Line 1: | Line 1: | ||
<div style="position:fixed;left:0;top:0"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:Cobson.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
In second-order set theories, such as Morse-Kelley set theory, a proper class is a collection of objects which is too large to be a set - either because that would cause a paradox, or because it contains another proper class. The axiom of limitation of size implies that any two proper classes can be put in bijection, implying they all have "size \(\mathrm{Ord}\)". Russel's paradox combined with the axiom of regularity ensure that \(V\), the class of all sets, is a proper class, and the [[Burali–Forti paradox]] shows that \(\mathrm{Ord}\). Also, all inner models, such as \(L\), are proper classes. |
In second-order set theories, such as Morse-Kelley set theory, a proper class is a collection of objects which is too large to be a set - either because that would cause a paradox, or because it contains another proper class. The axiom of limitation of size implies that any two proper classes can be put in bijection, implying they all have "size \(\mathrm{Ord}\)". Russel's paradox combined with the axiom of regularity ensure that \(V\), the class of all sets, is a proper class, and the [[Burali–Forti paradox]] shows that \(\mathrm{Ord}\). Also, all inner models, such as \(L\), are proper classes. |
||