ordinal numbers


The ordinal numbers are a way of measuring the size of well-ordered sets. They give a way of talking about different sizes of infinity. They are needed to construct the cardinal numbers, which measure the sizes of sets more generally.


This concept has the prerequisites:


  • Define what it means for a set to be an ordinal
  • Know that the ordinals can be divided into limit and successor ordinals
  • Show that the subset relation is a well ordering on the ordinals
  • Define what it means for two well-ordered sets to be isomorphic
  • Show that every well-ordered set is isomorphic to a unique ordinal
  • Show that for every ordinal, there is a larger ordinal

Core resources (read/watch one of the following)


Notes on Set Theory (2013)


See also

-No Additional Notes-