The difference between Denumerable and Uncountable set


Denumerable is also adjective with the meaning: capable of being assigned a bijection to the natural numbers. applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.

Uncountable set is also noun with the meaning: a set, containing infinite number of elements, whose elements can not be mapped one-to-one to the natural numbers. a set with a cardinality greater than that of the set of natural numbers.

check bellow for the other definitions of Denumerable and Uncountable set

  1. Denumerable as an adjective (mathematics):

    Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.

    Examples:

    "The empty set is not denumerable because it is finite; the rational numbers are, surprisingly, denumerable because every possible fraction can be assigned a natural number and vice versa."

  1. Uncountable set as a noun (mathematics):

    A set, containing infinite number of elements, whose elements can not be mapped one-to-one to the natural numbers. A set with a cardinality greater than that of the set of natural numbers.

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