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The article claims that "comparison" is the only valid operator on nominal numbers, and then restricts "comparison" to the equality operator '='. However, don't nominal numbers in practice have a total order on them, resulting in a less-than operator '<'? -- Damian Yerrick 17:03, 1 December 2005 (UTC) reply

No. Remember that these entities are barely numbers to begin with. The '<' & '>' operators only hold if they were serial numbers. DV8 2XL 17:48, 1 December 2005 (UTC) reply

OK, I get the point. I'll continue my question in ordinal number. -- Damian Yerrick 20:51, 1 December 2005 (UTC) reply

I've added further clarification along these lines: you can always use any number as an integer, but the point is that this is not meaningful.

Nbarth ( email) ( talk) 14:43, 1 March 2008 (UTC) reply

Although comparing nominal numbers with operator < doesn't make sense semantically, there are cases where they are compared as such to speed up lookups. A concrete example is a library. A book with Dewey Decimal code 004.21 isn't "less than" a book with Dewey Decimal code 500.21, but the books are arranged in order to be easy to find. In relational databases, many tables are given primary keys. A primary key identifies the row it's associated with uniquely, and in some cases has no semantic value at all. However, the primary key is indexed so rows can be looked up by primary key, and so the primary key can be used as a reference to that row. Should the sorting of nominal numbers for ease of access be mentioned in this article? —Preceding unsigned comment added by Joeyadams ( talk • contribs) 01:31, 12 January 2010 (UTC) reply

DV8 2XL removed the following paragraph from the article and asked me to discuss in talk why I added it:

If nominal numbers are a string of numerals (such as digits or letters), then additional digitwise operations can be defined on them. For instance, applying some total order on the numbers, such as a lexicographic order on the numerals, allows for collation of the numbers as ordinal numbers. Assigning a numeric value to each distinct numeral allows for calculations on the digits within a nominal number for redundancy checks, such as checksums to determine if the number is valid, that is, to verify its membership in a certain defined set.

If converting nominal numbers to digit strings for use as ordinal numbers is not to be discussed in Nominal number, then neither is converting nominal numbers to digit strings for use in a redundancy check. Would you please also delete that part? -- Damian Yerrick 21:53, 1 December 2005 (UTC) reply

In a bloody rush I made an bad mistake, I am re-inseting that paragraph and I beg your pardon. An unacceptable act of haste on my part DV8 2XL 22:22, 1 December 2005 (UTC) reply

Thank you. -- Damian Yerrick 22:26, 1 December 2005 (UTC) reply

I have refactored and cut down this article; most of the examples are wrong (telephone numbers and zip codes, for example, have a clear internal structure, and both correllate to externals such as geography and telcos), and two sections of the previous text directly contradicted one another. I've also mentioned that the term "nominal number" appears to be a neologism used in schools, rather than a term used by mathematicians; it may be derived from the term " nominal measurement" (or equivalently, " nominal data") used in statistics; however, statisticians and other mathematicians do not, as far as I know, regard the numbers used in nominal measurement as a special "kind of number", just as a mapping of classes to numbers. [1]

I've also had to reduce/remove/refactor material in serial number by the same contributor, which seemed to assign a mathematical significance to the serial number arithmetic defined in RFC 1982 far beyond that intended by its authors, and contained a substantial verbatim extract from that RFC.

-- The Anome 12:22, 15 January 2006 (UTC) reply

I've continued in this vein, indicating that the term has limited use, and distinguishing between a broad sense ("any string used for identification") and a narrow sense ("a string that conveys no information beyond identification"), and given extensive examples.

Nbarth ( email) ( talk) 14:34, 1 March 2008 (UTC) reply

Another good example is the game of Sudoku. The numbers 1 to 9 are used, but they have no numerical significance, they might as well be 9 different colours. 131.251.134.152 ( talk) 20:02, 22 October 2009 (UTC) reply

Suggesting to merge with Numbering scheme -- Krauss ( talk) 00:34, 4 September 2016 (UTC) reply