On the impossibility of a fixed point proof of the fundamental theorem of algebra. Seminar on mathematical analysis
(1985) In Seminar on mathematical analysis (Cluj-Napoca, 1985), p.157-161- Abstract
- The author shows that the proofs of \n B. H. Arnold\en [Amer. Math. Monthly 56 (1949), 465--466; MR0031725 (11,195h)] and \n I. Niven\en [ibid. 57 (1950), 246--248; MR0035738 (12,4c)] of the fundamental theorem of algebra, based on the Brouwer fixed point theorem, are incomplete. Both Arnold and Niven recognized that the proofs are invalid, and they remarked that no easy remedy seems to save their proofs.
In his note the author shows that it is impossible to prove the fundamental theorem of algebra using the method of these authors.
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http://lup.lub.lu.se/record/1467475
- author
- Aleman, Alexandru ^{LU}
- publishing date
- 1985
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Seminar on mathematical analysis (Cluj-Napoca, 1985),
- pages
- 157 - 161
- language
- English
- LU publication?
- no
- id
- 7d15cb08-06bd-471d-98c2-29b3521a8e17 (old id 1467475)
- date added to LUP
- 2009-09-16 14:50:11
- date last changed
- 2018-11-21 21:18:51
@article{7d15cb08-06bd-471d-98c2-29b3521a8e17, abstract = {The author shows that the proofs of \n B. H. Arnold\en [Amer. Math. Monthly 56 (1949), 465--466; MR0031725 (11,195h)] and \n I. Niven\en [ibid. 57 (1950), 246--248; MR0035738 (12,4c)] of the fundamental theorem of algebra, based on the Brouwer fixed point theorem, are incomplete. Both Arnold and Niven recognized that the proofs are invalid, and they remarked that no easy remedy seems to save their proofs.<br/><br> <br/><br> In his note the author shows that it is impossible to prove the fundamental theorem of algebra using the method of these authors.}, author = {Aleman, Alexandru}, language = {eng}, pages = {157--161}, series = {Seminar on mathematical analysis (Cluj-Napoca, 1985),}, title = {On the impossibility of a fixed point proof of the fundamental theorem of algebra. Seminar on mathematical analysis}, year = {1985}, }