The vice: Some historically inspired and proof-generated steps to limits of sequences

Educational Studies in Mathematics

Volumn 60, Issue 3, 2005, Pages 269-295

  Burn, Bob ^a  

^a NONE   (United Kingdom)

Author keywords

Archimedean postulate; As small as one may wish; Inequality; Limit; Sequence; Sufficiently large

Indexed keywords

EID: 28144438883     PISSN: 00131954     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10649-005-7923-6     Document Type: Article

References (25)

1. Baron, M.E.: 1969, The Origins of the Infinitesimal. Calculus, Pergamon, Oxford.
2. Burkill, J.C.: 1962, A First Course in Mathematical. Analysis, Cambridge University Press, Cambridge.
3. Burn, B.: 2003, 'Limits - a secondary school view', Proceedings of the British Society for Research into Learning Mathematics, Vol. 23, No. 3, pp. 13-17.
4. Burn, R.P.: 1982, A Pathway to Number Theory, 2nd ed. (1997), Cambridge University Press, Cambridge.
5. Burn, R.P.: 1985, Groups: A Path to Geometry, Cambridge University Press, Cambridge.
6. Burn, R.P.: 1992, Numbers and Functions: Steps into Analysis, 2nd ed. (2000), Cambridge University Press, Cambridge.
7. Cauchy, A.-L.: 1821, Analyse algébrique, Paris. Reprinted 1989, Éditions Jacques Gabay, Sceaux.
8. Cornu, B.: 1991, 'Limits', in D. Tall (ed.), Advanced Mathematical Thinking, chapter 10, Kluwer Academic Press, Dordrecht.
9. Davis, R.B. and Vinner, S.: 1986, 'The notion of limit: Some seemingly unavoidable misconception stages', Journal of Mathematical Behaviour 5, 281-303.
10. Dijksterhuis, E.J.: 1987, Archimedes, Princeton University Press, Princeton, NJ.
11. Fauvel, J. and Gray, J.: 1987, The History of Mathematics, a Reader, Open University.
12. Freudenthal, H.: 1973, 'What groups mean in mathematics', in A.G. Howson (ed.), Developments in Mathematics Education, Cambridge University Press, Cambridge.
13. Gregory of St Vincent: 1647, Opus geometricum quadraturae circuli et sectionum coni, decem libris compmhensum, Antwerp.
14. Heath, T.L.: 1956, The Thirteen Books of Euclid's Elements, Dover, New York.
15. Knopp, K.: 1928, Theory and Application of Infinite Series, Blackie, Glasgow.
16. Mahoney, M.S.: 1994, The Mathematical Career of Pierre de Fermat, Princeton University Press, Princeton, NJ.
17. Mamona-Downs, J.: 2001, 'Letting the intuitive bear on the formal; a didactical approach for the understanding of the limit of a sequence', Educational Studies in Mathematics 48(2-3), 259-288.
18. Pourciau, B.: 2001, 'Newton and the notion of limit', Historia Mathematica 28, 18-30.
19. Sierpinska, A.: 1990, 'Some remarks on understanding in mathematics', For the Learning of Mathematics 10(3), 24-41.
20. Struik, D.J.: 1969, A Source Book in Mathematics 1200-1800, Harvard University Press, Cambridge, MA.
21. Toeplitz, O.: 1963, The Calculus, a Genetic Approach, Chicago University Press.
22. Viète, F.: 1593, Variorum de Rebus Mathematicis Responsorum, liber VIII, Paris,
23. reprinted 1646, Opera Mathematica, F. van Schooten (ed.), Leiden, pp. 347-435.
24. Wallis, J.: 1655, Arithmetica Infinitorum, Oxford,
25. reprinted 1695, Opera Mathematica, Oxford, reprinted 1972, Hildesheim, Olms.