Cardinal Set

A Cardinal Set is a Non-Empty Ordered Set composed solely of Cardinal Values.

• Context:
  • It must have:
    • a First Member.
    • a Second Member.
    • a Final Member.
  • …
• Example(s):
  • {First Member < Second Member < Second-to-Last Member < Final Member}.
  • {One < Two < Three}.
  • {First Member}, a Degenerate Set.
  • …
• Counter-Example(s):
  • {Large < Medium < Small}, an Ordered Set whose Members are not Cardinal Values.
  • {Winner < Loser}, because the Order is subjectively determined.
  • {}, an Empty Set.
• See: Ordered Set, Numeric Interval.

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References

• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=cardinal%20number
  • S: (n) cardinal number, cardinal (the number of elements in a mathematical set; denotes a quantity but not the order)
• http://en.wiktionary.org/wiki/cardinal_number
  • Noun
    • 1. A number used to denote quantity; a counting number.
      • The smallest cardinal numbers are 0, 1, 2, and 3.
      • The cardinal number "three" can be represented as "3" or "three".
    • 2. (mathematics) A generalized kind of number used to denote the size of a set, including infinite sets.
    • 3. (grammar) A word that expresses a countable quantity; a cardinal numeral. “Three" is a cardinal number, while "third" is an ordinal number.

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