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THE PROOF OF A FUNCTIONAL EQUATION BY USING GRAPHS AND SET THEORY

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  • Deniz Can Karacelebi Izmir Bahcesehir 50.th Year Science and Technology High School

DOI:

https://doi.org/10.58445/rars.1848

Keywords:

set theory, cardinal, ordinal, graph theory, functions

Abstract

There are different ways to approach in solving functional equation problems in
mathematics. In this paper, Set theory and graph theory techniques, which are rarely
encountered in the solutions of typical function problems, are used to construct our
proof. At the same time, our approach differs from those commonly used problems
solved by graph theory, as the solution is reached by examining uncountable graphs
with the help of set theory.

References

Erdős, P. and Hajnal, A. (1966). On chromatic number of graphs and setsystems.

Acta Mathematica Academiac Scientiarum Hungaricae, 17:61–99.

Weiss, W. A. R. (2008). An introduction to set theory. CreateSpace Independent

Publishing Platform, Online.

Goldmakher, L. (2013). The cantor-schroeder-bernstein theorem. https://web.

williams.edu/Mathematics/lg5/CanBer.pdf.

Dirac, G. A. (1952). Some theorems on abstract graphs. Proceedings of the

London Mathematical Society, 3(1):69–81.

Rapaport, W. J. (2009). A set-theoretical definition of graphs. https://cse. buffalo.

edu/ rapaport/191/graphasset.html.

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Posted

2024-10-24

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