uncountability造句

• For a proof, see Cantor's first uncountability proof.
• This contradicts the original assumption, and proves the uncountability theorem.
• Infinite divisibility alone implies infiniteness but not uncountability, as the rational numbers exemplify.
• See Cantor's first uncountability proof.
• Cantor does not explicitly prove his uncountability theorem, which follows easily from his second theorem.
• Without the uncountability theorem, the article needed a title that did not refer to this theorem.
• The uncountability theorem demonstrated that one-to-one correspondences can be used to analyze infinite sets.
• So it is not obvious which one is the appropriate generalization of " uncountability " when the axiom fails.
• The finite intersection property is useful in formulating an alternative definition of uncountability of the real numbers ( see next section)
• However, I'm asked here what happens when we allow uncountability, and I haven't really got a clue!
• Dedekind sent Cantor this proof in reply to Cantor's letter that announced the uncountability theorem and proved it using infinitely many sequences.
• For example, they have discovered that Cantor was advised to leave out his uncountability theorem in the article he submitted; he added it during proofreading.
• In addition, they have looked at the article's legacy namely, the impact of the uncountability theorem and the concept of countability on mathematics.
• They must be taken into account to construct a valid proof, applying his 1891 diagonal argument to decimal expansions, of the uncountability of the unit interval.
• The uncountability of a set is closely related to its cardinal number : a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.
• In British English, these are " sugar strands " or " hundreds-and-thousands " ( the latter term alludes to their supposed uncountability ).
• Weierstrass advised Cantor to leave his uncountability theorem out of the article he submitted, but Weierstrass also told Cantor that he could add it as a marginal note during proofreading, which he did.
• Cantor gave two proofs that the cardinality of the set of integers is strictly smaller than that of the set of real numbers ( see Cantor's first uncountability proof and Cantor's diagonal argument ).
• However, I " have " been looking at the " Cantor's first uncountability proof " article and in particular the talk ) 00 : 30, 25 November 2008 ( UTC)
• Cantor's correspondence with Richard Dedekind shows the development of his ideas and reveals that he had a choice between two proofs, one that uses the uncountability of the real numbers and one that does not.