Bridge to abstract mathematics /:
Of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Washington, DC] :
Mathematical Association of America,
©2012.
|
| Schriftenreihe: | MAA textbooks.
|
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | Of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises |
| Beschreibung: | 1 online resource (xix, 232 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (page 223) and index. |
| ISBN: | 9781614446064 1614446067 9781470453039 1470453037 |
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MARC
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| 505 | 0 | |a Front cover -- copyright page -- title page -- Contents -- Some Notes on Notation -- To the Students -- To Those Beginning the Journey into Proof Writing -- How to Use This Text -- Do the Exercises! -- Acknowledgments -- For the Professors -- To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines -- I THE AXIOMATIC METHOD -- Introduction -- The History of Numbers -- The Algebra of Numbers -- The Axiomatic Method -- Parallel Mathematical Universes -- Statements in Mathematics -- Mathematical Statements | |
| 505 | 8 | |a Mathematical ConnectivesSymbolic Logic -- Compound Statements in English -- Predicates and Quantifiers -- Supplemental Exercises -- Proofs in Mathematics -- What is Mathematics? -- Direct Proof -- Contraposition and Proof by Contradiction -- Proof by Induction -- Proof by Complete Induction -- Examples and Counterexamples -- Supplemental Exercises -- How to THINK about mathematics: A Summary -- How to COMMUNICATE mathematics: A Summary -- How to DO mathematics: A Summary -- II SET THEORY -- Basic Set Operations -- Introduction -- Subsets | |
| 505 | 8 | |a Intersections and UnionsIntersections and Unions of Arbitrary Collections -- Differences and Complements -- Power Sets -- Russell's Paradox -- Supplemental Exercises -- Functions -- Functions as Rules -- Cartesian Products, Relations, and Functions -- Injective, Surjective, and Bijective Functions -- Compositions of Functions -- Inverse Functions and Inverse Images of Functions -- Another Approach to Compositions -- Supplemental Exercises -- Relations on a Set -- Properties of Relations -- Order Relations -- Equivalence Relations | |
| 505 | 8 | |a Supplemental ExercisesCardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems -- Introduction: A Road Map -- Primary Properties of Number Systems -- Secondary Properties -- Isomorphisms and Embeddings -- Archimedean Ordered Fields -- Supplemental Exercises -- The Natural Numbers -- Introduction -- Zero, the Natural Numbers, and Addition -- Multiplication -- Supplemental Exercises | |
| 505 | 8 | |a Summary of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises | |
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| author | Oberste-Vorth, Ralph W., 1959- |
| author2 | Mouzakitis, Aristides Lawrence, Bonita A., 1957- |
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| contents | Front cover -- copyright page -- title page -- Contents -- Some Notes on Notation -- To the Students -- To Those Beginning the Journey into Proof Writing -- How to Use This Text -- Do the Exercises! -- Acknowledgments -- For the Professors -- To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines -- I THE AXIOMATIC METHOD -- Introduction -- The History of Numbers -- The Algebra of Numbers -- The Axiomatic Method -- Parallel Mathematical Universes -- Statements in Mathematics -- Mathematical Statements Mathematical ConnectivesSymbolic Logic -- Compound Statements in English -- Predicates and Quantifiers -- Supplemental Exercises -- Proofs in Mathematics -- What is Mathematics? -- Direct Proof -- Contraposition and Proof by Contradiction -- Proof by Induction -- Proof by Complete Induction -- Examples and Counterexamples -- Supplemental Exercises -- How to THINK about mathematics: A Summary -- How to COMMUNICATE mathematics: A Summary -- How to DO mathematics: A Summary -- II SET THEORY -- Basic Set Operations -- Introduction -- Subsets Intersections and UnionsIntersections and Unions of Arbitrary Collections -- Differences and Complements -- Power Sets -- Russell's Paradox -- Supplemental Exercises -- Functions -- Functions as Rules -- Cartesian Products, Relations, and Functions -- Injective, Surjective, and Bijective Functions -- Compositions of Functions -- Inverse Functions and Inverse Images of Functions -- Another Approach to Compositions -- Supplemental Exercises -- Relations on a Set -- Properties of Relations -- Order Relations -- Equivalence Relations Supplemental ExercisesCardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems -- Introduction: A Road Map -- Primary Properties of Number Systems -- Secondary Properties -- Isomorphisms and Embeddings -- Archimedean Ordered Fields -- Supplemental Exercises -- The Natural Numbers -- Introduction -- Zero, the Natural Numbers, and Addition -- Multiplication -- Supplemental Exercises Summary of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises |
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| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
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| discipline | Mathematik |
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| genre | Textbooks fast |
| genre_facet | Textbooks |
| id | ZDB-4-EBA-ocn818906408 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:04Z |
| institution | BVB |
| isbn | 9781614446064 1614446067 9781470453039 1470453037 |
| language | English |
| oclc_num | 818906408 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 232 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Mathematical Association of America, |
| record_format | marc |
| series | MAA textbooks. |
| series2 | MAA textbooks |
| spelling | Oberste-Vorth, Ralph W., 1959- https://id.oclc.org/worldcat/entity/E39PCjMqcGxvQ4WgWJdbWH8RDq http://id.loc.gov/authorities/names/no2013031151 Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence. [Washington, DC] : Mathematical Association of America, ©2012. 1 online resource (xix, 232 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file MAA textbooks Includes bibliographical references (page 223) and index. Print version record. Front cover -- copyright page -- title page -- Contents -- Some Notes on Notation -- To the Students -- To Those Beginning the Journey into Proof Writing -- How to Use This Text -- Do the Exercises! -- Acknowledgments -- For the Professors -- To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines -- I THE AXIOMATIC METHOD -- Introduction -- The History of Numbers -- The Algebra of Numbers -- The Axiomatic Method -- Parallel Mathematical Universes -- Statements in Mathematics -- Mathematical Statements Mathematical ConnectivesSymbolic Logic -- Compound Statements in English -- Predicates and Quantifiers -- Supplemental Exercises -- Proofs in Mathematics -- What is Mathematics? -- Direct Proof -- Contraposition and Proof by Contradiction -- Proof by Induction -- Proof by Complete Induction -- Examples and Counterexamples -- Supplemental Exercises -- How to THINK about mathematics: A Summary -- How to COMMUNICATE mathematics: A Summary -- How to DO mathematics: A Summary -- II SET THEORY -- Basic Set Operations -- Introduction -- Subsets Intersections and UnionsIntersections and Unions of Arbitrary Collections -- Differences and Complements -- Power Sets -- Russell's Paradox -- Supplemental Exercises -- Functions -- Functions as Rules -- Cartesian Products, Relations, and Functions -- Injective, Surjective, and Bijective Functions -- Compositions of Functions -- Inverse Functions and Inverse Images of Functions -- Another Approach to Compositions -- Supplemental Exercises -- Relations on a Set -- Properties of Relations -- Order Relations -- Equivalence Relations Supplemental ExercisesCardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems -- Introduction: A Road Map -- Primary Properties of Number Systems -- Secondary Properties -- Isomorphisms and Embeddings -- Archimedean Ordered Fields -- Supplemental Exercises -- The Natural Numbers -- Introduction -- Zero, the Natural Numbers, and Addition -- Multiplication -- Supplemental Exercises Summary of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises Of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises Logic, Symbolic and mathematical Textbooks. Mathematics Textbooks. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Mathematics fast Beweis gnd http://d-nb.info/gnd/4132532-1 Mathematik gnd http://d-nb.info/gnd/4037944-9 Textbooks fast Mouzakitis, Aristides. Lawrence, Bonita A., 1957- https://id.oclc.org/worldcat/entity/E39PCjyr99R3vwjyM3j9Kh4QMd http://id.loc.gov/authorities/names/no2013031145 has work: Bridge to abstract mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGYMFj4xhCdm6tfKDgMWym https://id.oclc.org/worldcat/ontology/hasWork Print version: Oberste-Vorth, Ralph W., 1959- Bridge to abstract mathematics. [Washington, DC] : Mathematical Association of America, ©2012 9780883857793 (OCoLC)809028598 MAA textbooks. http://id.loc.gov/authorities/names/no2008011989 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=3934669 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=481551 Volltext |
| spellingShingle | Oberste-Vorth, Ralph W., 1959- Bridge to abstract mathematics / MAA textbooks. Front cover -- copyright page -- title page -- Contents -- Some Notes on Notation -- To the Students -- To Those Beginning the Journey into Proof Writing -- How to Use This Text -- Do the Exercises! -- Acknowledgments -- For the Professors -- To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines -- I THE AXIOMATIC METHOD -- Introduction -- The History of Numbers -- The Algebra of Numbers -- The Axiomatic Method -- Parallel Mathematical Universes -- Statements in Mathematics -- Mathematical Statements Mathematical ConnectivesSymbolic Logic -- Compound Statements in English -- Predicates and Quantifiers -- Supplemental Exercises -- Proofs in Mathematics -- What is Mathematics? -- Direct Proof -- Contraposition and Proof by Contradiction -- Proof by Induction -- Proof by Complete Induction -- Examples and Counterexamples -- Supplemental Exercises -- How to THINK about mathematics: A Summary -- How to COMMUNICATE mathematics: A Summary -- How to DO mathematics: A Summary -- II SET THEORY -- Basic Set Operations -- Introduction -- Subsets Intersections and UnionsIntersections and Unions of Arbitrary Collections -- Differences and Complements -- Power Sets -- Russell's Paradox -- Supplemental Exercises -- Functions -- Functions as Rules -- Cartesian Products, Relations, and Functions -- Injective, Surjective, and Bijective Functions -- Compositions of Functions -- Inverse Functions and Inverse Images of Functions -- Another Approach to Compositions -- Supplemental Exercises -- Relations on a Set -- Properties of Relations -- Order Relations -- Equivalence Relations Supplemental ExercisesCardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems -- Introduction: A Road Map -- Primary Properties of Number Systems -- Secondary Properties -- Isomorphisms and Embeddings -- Archimedean Ordered Fields -- Supplemental Exercises -- The Natural Numbers -- Introduction -- Zero, the Natural Numbers, and Addition -- Multiplication -- Supplemental Exercises Summary of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises Logic, Symbolic and mathematical Textbooks. Mathematics Textbooks. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Mathematics fast Beweis gnd http://d-nb.info/gnd/4132532-1 Mathematik gnd http://d-nb.info/gnd/4037944-9 |
| subject_GND | http://d-nb.info/gnd/4132532-1 http://d-nb.info/gnd/4037944-9 |
| title | Bridge to abstract mathematics / |
| title_auth | Bridge to abstract mathematics / |
| title_exact_search | Bridge to abstract mathematics / |
| title_full | Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence. |
| title_fullStr | Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence. |
| title_full_unstemmed | Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence. |
| title_short | Bridge to abstract mathematics / |
| title_sort | bridge to abstract mathematics |
| topic | Logic, Symbolic and mathematical Textbooks. Mathematics Textbooks. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Mathematics fast Beweis gnd http://d-nb.info/gnd/4132532-1 Mathematik gnd http://d-nb.info/gnd/4037944-9 |
| topic_facet | Logic, Symbolic and mathematical Textbooks. Mathematics Textbooks. MATHEMATICS Infinity. MATHEMATICS Logic. Logic, Symbolic and mathematical Mathematics Beweis Mathematik Textbooks |
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