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Cantor's diagonal argument
Cantor's diagonal argument, or diagonalization, is an 1891 proof by Georg Cantor that no list can contain every real number in [0,1], showing the reals are uncountable.
Cardinality of the continuum
The cardinality of the continuum, also called the power of the continuum, is the size of the set of real numbers, strictly larger than that of the natural numbers.
Infinite set
An infinite set is a set that is not finite, so its elements cannot be counted with a natural number; Cantor showed in 1874 that infinities come in different sizes.
Infinity
Infinity is the condition of being without any finite bound in size, extent, or quantity, appearing in mathematics as both endless process and completed infinite objects.