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Finite to Infinite - An Expository on Nonstandard Analysis
Alagu. S1 , R. Kala2
- Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli, Tamilnadu, India.
- Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli, Tamilnadu, India.
Section:Review Paper, Product Type: Isroset-Journal
Vol.5 ,
Issue.3 , pp.133-135, Jun-2018
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v5i3.133135
Online published on Jun 30, 2018
Copyright © Alagu. S, R. Kala . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: Alagu. S, R. Kala, “Finite to Infinite - An Expository on Nonstandard Analysis,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.133-135, 2018.
MLA Style Citation: Alagu. S, R. Kala "Finite to Infinite - An Expository on Nonstandard Analysis." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.3 (2018): 133-135.
APA Style Citation: Alagu. S, R. Kala, (2018). Finite to Infinite - An Expository on Nonstandard Analysis. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(3), 133-135.
BibTex Style Citation:
@article{S_2018,
author = {Alagu. S, R. Kala},
title = {Finite to Infinite - An Expository on Nonstandard Analysis},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {6 2018},
volume = {5},
Issue = {3},
month = {6},
year = {2018},
issn = {2347-2693},
pages = {133-135},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=685},
doi = {https://doi.org/10.26438/ijcse/v5i3.133135}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i3.133135}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=685
TI - Finite to Infinite - An Expository on Nonstandard Analysis
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Alagu. S, R. Kala
PY - 2018
DA - 2018/06/30
PB - IJCSE, Indore, INDIA
SP - 133-135
IS - 3
VL - 5
SN - 2347-2693
ER -
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Abstract :
Nonstandard analysis is a branch of Mathematics introduced by Abraham Robinson[1] in 1966. In 1977, Edward Nelson[2] gave an axiomatic approach to Non-standard analysis. In many instances, analysis on infinite sets can be reduced to a finiteness argument using Nonstandard methods. In this expository article, we present an introduction to the theory and indicate an application to infinite graphs. The application is to a result by De Bruijn and Paul R. Erdos that it is enough to study colouring problem only in finite graphs.
Key-Words / Index Term :
Nonstandard analysis, Graphs, Colouring
References :
[1] Abraham Robinson, Nonstandard Analysis, North Holland Publishing Company, 1966.
[2] Edward Nelson, Internal Set theory, a new approach to NSA, Bull. Amer. Math. Soc.,83(1977) pp.1165-1198.
[3] Alain Robert, Nonstandard Analysis, John Wiley and sons, 1985.
[4] A.E.Hurd and P.A.Loeb, An Introduction to Non Standard Real Analysis, Academic Press (1985).
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