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
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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."
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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.