عنوان

An introduction to mathematical reasoning :

0521592690

0521597188 (pb)

9780521592697

9780521597180 (pb)

dltt

An introduction to mathematical reasoning :

[Book]

numbers, sets, and functions /

Peter J. Eccles

New York :

Cambridge University Press,

1997

xii, 350 p. :

ill. ;

24 cm

Includes bibliographical references (p. 345) and index

Pt. I. Mathematical statements and proofs. 1. The language of mathematics. 2. Implications. 3. Proofs. 4. Proof by contradiction. 5. The induction principle -- Pt. II. Sets and functions. 6. The language of set theory. 7. Quantifiers. 8. Functions. 9. Injections, surjections and bijections -- Pt. III. Numbers and counting. 10. Counting. 11. Properties of finite sets. 12. Counting functions and subsets. 13. Number systems. 14. Counting infinite sets -- Pt. IV. Arithmetic. 15. The division theorem. 16. The Euclidean algorithm. 17. Consequences of the Euclidean algorithm. 18. Linear diophantine equations -- Pt. V. Modular arithmetic. 19. Congruence of integers. 20. Linear congruences. 21. Congruence classes and the arithmetic of remainders. 22. Partitions and equivalence relations -- Pt. VI. Prime numbers. 23. The sequence of prime numbers. 24. Congruence modulo a prime

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Mathematical reasoning

Proof theory

Eccles, Peter J.,1945-

20130220075616.0

[Book]

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