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Nominal numbers are numbers used for identification only. They do not indicate quantity, rank, or any other measurement. However they may encode information. The properties of nominal numbers are the minimum required to refer to an entity as a number.

Examples of nominal numbers include; sport jersey numbers; telephone numbers; zip codes; transportation route numbers; etc.

Operations with nominal numbers

A Nominal number is a numeral, or a string of numerals that is used for identification only, so that the only valid operation that may be carried out with nominal numbers is comparison. That is, two or more nominal numbers can be compared to determine if they are identical; while this may seem trite, it is a distinction important for computer science.

The converse of this is that any other mathematical operation done with or upon nominal numbers yields nonsense. The pseudo-science of numerology rejects this, instead declaring the opposite as a fundamental tenet.

Comparison

Any two serial numbers, s1 and s2, may be compared. The definition of the result of this comparison is as follows.

For the purposes of this definition, consider two integers, i1 and i2, from the unbounded set of non-negative integers, such that i1 and s1 have the same numeric value, as do i2 and s2. Arithmetic and comparisons applied to i1 and i2 use ordinary unbounded integer arithmetic.

Then, s1 is said to be equal to s2 if and only if i1 is equal to i2, in all other cases, s1 is not equal to s2.

However various calculations can be done with 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.

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