properties of ordinal arithmetic
, for the former has a top element and the latter does not.
, for the former is , which consists an element such that for all , and the latter is , which is just , and which does not consist such an element
, for the former is and the latter is , and the rest of the follows from the previous counterexample.
All of the properties above can be proved using transfinite induction. For a proof of the first property, please see this link (http://planetmath.org/ExampleOfTransfiniteInduction).
|Title||properties of ordinal arithmetic|
|Date of creation||2013-03-22 17:51:05|
|Last modified on||2013-03-22 17:51:05|
|Last modified by||CWoo (3771)|