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Denumerable vs Indenumerable - What's the difference?

denumerable | indenumerable |

As adjectives the difference between denumerable and indenumerable

is that denumerable is capable of being assigned numbers from the natural numbers. Especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable while indenumerable is not denumerable.

denumerable

English

(wikipedia denumerable)

Adjective

(-)
  • (mathematics) Capable of being assigned numbers from the natural numbers. Especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable.
    • The empty set is denumerable''' because it is finite; the rational numbers are, surprisingly, '''denumerable because every possible fraction can be assigned a number.

    Derived terms

    *

    Synonyms

    * countable

    See also

    * countable set * uncountable set

    indenumerable

    English

    Adjective

    (-)
  • Not denumerable.
  • * 1963 , Hao Wang, Provability, Computability and Reflection , Elsevier, page 563
    • From the fact that no enumeration can exhaust all sets of positive integers, Cantor infers that the set of all sets of positive integers is absolutely indenumerable .