The terms "ordinal number" and "cardinal number" has advanced mathematical
meanings in the theory of infinite sets and transfinite numbers, but the words
also have ancient meanings in grammar. The semantics of a cardinal number is to
count the elements of a finite set, and the semantics of an ordinal number is
to identify a single element. This century is the twentyfirst century. That is
a 1-origin ordinal number. The number of whole centuries that have passed so
far is 20. That is a 0-origin cardinal number. /Bo.
Den 12:49 lørdag den 19. maj 2018 skrev R.E. Boss <[email protected]>:
> A solution to the problem is to distinguish between the ordinal numbers
> (first,
> second, and so on) and cardinal numbers (zero, one, and so on). The first
> ordinal number is "first", and the first cardinal number is "zero". Cardinal
> number are for indexing, not for counting. Thanks. Bo.
I like that very much, although I read different things in
https://www.wikiwand.com/en/Ordinal_number
"A natural number (which, in this context, includes the number 0) can be used
for two purposes: to describe the size of a set, or to describe the position of
an element in a sequence."
(...)
" Whereas the notion of cardinal number is associated with a set with no
particular structure on it, the ordinals are intimately linked with the special
kind of sets that are called well-ordered (...) "
(...)
" Ordinals may be used to label the elements of any given well-ordered set (the
smallest element being labelled 0, the one after that 1, the next one 2, "and
so on") and to measure the "length" of the whole set by the least ordinal that
is not a label for an element of the set."
See also https://www.wikiwand.com/en/Cardinal_number .
R.E. Boss
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