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Denumerable Set. A set is denumerable iff it is equipollent to the finite ordinal numbers. Moore 1982, p. 6; Rubin 1967, p. 107; Suppes 1972, pp. 151-152. However, Ciesielski 1997, p. 64 calls this property "countable." The set aleph0 is most commonly called "denumerable" to "countably infinite". Definition: "Denumerable" Most difficulties with the diagonal method revolve around the definition of the word "denumerable." As mentioned previous, the diagonal method is supposed to show that the rational numbers are denumerable, while the real numbers are not. But there is no way to understand the meaning of the term denumerable, until after you have applied the diagonal method. Many or most set theorists seldom use the word denumerable. In a quick perusal, I couldn't find use of it in Jech's book Set Theory or Kanamori's book on large cardinals. In a quick perusal, I couldn't find use of it in Jech's book Set Theory or Kanamori's book on large cardinals.

Chapter 5 Denumerable and Non-denumerable Sets Dedekind’s de nition of an in nite set is used to discuss properties of in nite sets and nite sets. It is proved, among other things, that denumerable sets are the smallest in size among the in nite sets. Properties and examples of denumerable sets and non-denumerable sets are given. Especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable. The empty set is denumerable because it is finite; the rational numbers are, surprisingly, denumerable because every possible fraction can be assigned a number. Definition of denumerable in thedictionary. Meaning of denumerable. What does denumerable mean? Information and translations of denumerable in the most comprehensive dictionary definitions resource on the web. Definition von denumerable im Englisch Englisch wörterbuch Capable of being assigned numbers from the natural numbers. Especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable. The fragment you quote is a definition. My question is in the other direction: Is it correct to say: if a set of sentences is denumerably categorical, then all denumerable models are isomorphic? Yes, by definition. What does this definition mean?

Definition 24. A set is denumerable if and only if it is equipollent to the set $\omega$ of all natural numbers. Theorem 43. Every denumerable set is infinite. page 191: Theorem 59. The set of real numbers is not denumerable. Denumerable Sets Definition: A set is denumerable iff it is of the same cardinality as ℕ. Also known as countably infinite. The cardinality of the denumerable sets is denoted ℵ 0 which is read as "aleph naught" or "aleph null". ℵ is the first letter of the Hebrew alphabet. One may be tempted to say, in analogy with finite sets, that all.

The point-set that the early intuitionists accepted as constructible was even smaller than the continuum outlined by the grammarian orientation; its power did not exceed the denumerable and so it could not be identified, even provisionally, with the power set of the natural numbers.