Assertion: real number | /r/HasProperty | uncountable
Facets:
value: as a set
type: OTHER
Source sentences:
text: But the Real numbers are "Uncountable".
text: The reals are uncountable; that is: there are strictly more real numbers than natural numbers, even though both sets are infinite.
text: The real numbers are uncountable.
text: Even though there are infinitely many real numbers and infinitely many integers, we can say that there are "more" real numbers than integers because the integers are countable and the real numbers are uncountable.
text: As a set, real numbers are uncountable while integers are countable.
text: As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.
text: In 1874, Georg Cantor proved that the algebraic numbers are countable and the real numbers are uncountable.
text: However, Cantor's diagonal argument proves that the real numbers (and therefore also the complex numbers) are uncountable.
text: In fact, I could even say that the reals were uncountable!