Finite Set

A Finite Set is a set (with Finite Set Members) whose Set Cardinality is an N0 Natural Number.

• Context:
  • It can range from being Finite Nonempty Set to being an Empty Set.
  • …
• Example(s):
  • The Empty Set, because Zero is an N0 Natural Number.
  • {1}, a Degenerate Set.
  • {1,2,3,4,5}.
  • …
• Counter-Example(s):
  • an Infinite Set.
• See: Countable Set.

---

---

References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Finite_set
  • In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. (The value n = 0 is allowed; that is, the empty set is finite.) An infinite set is a set which is not finite.
  • Equivalently, a set is finite if its cardinality, i.e., the number of its elements, is a natural number. More specifically, a set whose cardinality is n is also called an n-set. For instance, the set of integers between −15 and 3 (excluding the end points) has 17 elements, so it is finite; in fact, it is a 17-set.

---