Talk:Von Neumann cardinal assignment

Section on "initial ordinal"
The section "Initial ordinal of a cardinal" is also literally on ordinal number. If we really need both, let us make it a template.--Patrick 12:44, 9 June 2007 (UTC)


 * Over a year ago, I copied that section into this article for two reasons: (1) it is relevant to the topic of this article; and (2) I was afraid that the section would be deleted from the other article (which fortunately has not happened yet). A little redundancy never hurt anything (outside cryptology). Making a template would be a mistake. It would use another article to what purpose? Just to make these two a little shorter. And it would complicate everything, and make this text more vulnerable to being deleted or lost. I vote against your idea. JRSpriggs 09:51, 10 June 2007 (UTC)


 * In general duplication causes forking: improvements may be made to each copy, which means duplication of work, and no copy where all improvements are integrated.--Patrick 10:30, 10 June 2007 (UTC)


 * But you can tailor each section to its context. It would probably be awkward if the wording had to be exactly identical in two different contexts. JRSpriggs 11:20, 10 June 2007 (UTC)

Infimum
isn't it slightly misleading to say that the initial ordinal is the infimum of a set of ordinals? wouldn't it be more appropriate to place a minimum there (considering every set of ordinals has a smallest element, since, well, they're well-ordered).--87.99.27.160 (talk) 00:32, 10 March 2010 (UTC)


 * The article does not use the word "infimum", it says "smallest" which is a synonym for "least". "Minimum" would be misleading because, as you point, out this is a well-ordering (and thus a total ordering). In a total ordering, an element of a subset is minimal if and only if it is least. But in a partial ordering, there is at most one least element, but there may be more than one minimum element. If there are two different minimal elements, then they are incomparable. See greatest element and maximal element. JRSpriggs (talk) 10:12, 10 March 2010 (UTC)

Notation &omega;&alpha;
Is it worth mentioning that this notation isn't to be confused with the occasional usage of &omega;n to denote &omega;&uparrow;&uparrow;n? Some papers such as "Hydrae and Subsystems of Arithmetic", "A Note on Gentzen's Ordinal Assignment", and "A Model-Theoretic Approach to Ordinal Analysis" use &omega;n this way. C7XWiki (talk) 21:58, 3 September 2022 (UTC)


 * As long as we are clear and consistent within this article on how we use the notation, I think that that is enough. The other usage (of which I never heard before) is sufficiently rare that it would be more confusing to mention it than to just ignore it. JRSpriggs (talk) 00:18, 4 September 2022 (UTC)