Search
- Filter Results
- Location
- Classification
- Include attachments
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/01%3A_I-_Sets_Relations_Functions/1.04%3A_The_Size_of_Sets/1.4.11%3A_SummaryA set A is countable if its elements can be arranged in an enumeration, a one-way infinite list, i.e., when there is a surjective function f:\PosInt→A. To give a diagonal argument, w...A set A is countable if its elements can be arranged in an enumeration, a one-way infinite list, i.e., when there is a surjective function f:\PosInt→A. To give a diagonal argument, we assume that the set A in question is countable, and use a hypothetical enumeration to define an element of A which, by the very way we define it, is guaranteed to be different from every element in the enumeration.
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/01%3A_I-_Sets_Relations_Functions/1.04%3A_The_Size_of_Sets/1.4.08%3A_EquinumerosityIn general, infinite sets can be compared sizewise: A and B are the same size, or equinumerous, if there is a bijection between them.
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/zz%3A_Back_Matter/22%3A_Appendix_B%3A_Induction
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/02%3A_II-_First-order_Logic/2.06%3A_The_Completeness_Theorem
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/zz%3A_Back_Matter/21%3A_Appendix_A%3A_Proofs/1.01%3A_A.1-_IntroductionBefore attempting a proof, it’s important to know what a proof is and how to construct one.
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/02%3A_II-_First-order_Logic/2.02%3A_Theories_and_Their_Models/2.2.05%3A_The_Theory_of_SetsAlmost all of mathematics can be developed in the theory of sets.
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/02%3A_II-_First-order_Logic/2.06%3A_The_Completeness_Theorem/2.6.07%3A_IdentityThe construction of the term model given in the preceding section is enough to establish completeness for first-order logic for sets Γ that do not contain =. It does not work, however, if...The construction of the term model given in the preceding section is enough to establish completeness for first-order logic for sets Γ that do not contain =. It does not work, however, if = is present. We can fix this using a construction known as “factoring.”
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/00%3A_Front_Matter/01%3A_TitlePageBook: Sets, Logic, Computation (Zach)
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/01%3A_I-_Sets_Relations_Functions/1.03%3A_Functions
- https://human.libretexts.org/Bookshelves/Philosophy/Sets_Logic_Computation_(Zach)/02%3A_II-_First-order_Logic/2.02%3A_Theories_and_Their_Models
