The Concept of the Mathematical Infinity and Economics

Author(s)
Bhekuzulu Khumalo

ABSTRACT

Mathematics is the basis of all science for the simple fact that it allows us to measure, counting in its basic sense is measuring. Mathematics is most useful when it is accurate. When we look at the concept of infinity we get new insights into mathematics and how it can be more accurate. This paper endeavors to show that understanding infinity will lead scientists, including economists to take into consideration another classification of variables over and above the traditional classification of continuous and discrete variables. This classification is the dimension of the variable. This problem would never have come to light if knowledge was not given a unit, the knowl, giving anything a unit allows it to be studied in a scientific manner. One finds that knowledge behaves as if it is a three dimensional variable and at other times as if it has infinite dimensions, and the mathematics has to be modified to deal with knowledge as it behaves differently. The reasons are explained hopefully fully in this paper to be grasped and understood. This paper is a follow up to a research note published in International Advances in Economic Research, titled “The Concept of the mathematical Infinity and Economics”.

Mathematics is the basis of all science for the simple fact that it allows us to measure, counting in its basic sense is measuring. Mathematics is most useful when it is accurate. When we look at the concept of infinity we get new insights into mathematics and how it can be more accurate. This paper endeavors to show that understanding infinity will lead scientists, including economists to take into consideration another classification of variables over and above the traditional classification of continuous and discrete variables. This classification is the dimension of the variable. This problem would never have come to light if knowledge was not given a unit, the knowl, giving anything a unit allows it to be studied in a scientific manner. One finds that knowledge behaves as if it is a three dimensional variable and at other times as if it has infinite dimensions, and the mathematics has to be modified to deal with knowledge as it behaves differently. The reasons are explained hopefully fully in this paper to be grasped and understood. This paper is a follow up to a research note published in International Advances in Economic Research, titled “The Concept of the mathematical Infinity and Economics”.

Cite this paper

B. Khumalo, "The Concept of the Mathematical Infinity and Economics,"*Modern Economy*, Vol. 3 No. 6, 2012, pp. 798-809. doi: 10.4236/me.2012.36102.

B. Khumalo, "The Concept of the Mathematical Infinity and Economics,"

References

[1] J. Mazur, “Euclid in the Rainforest: Discovering Universal Truth in Logic and Math,” Penguin Books, New York, 2005.

[2] D. J. Struik, “A Concise History of Mathematics,” Dover Publications, New York, 1967.

[3] R. Kaplan and E. Kaplan, “The Art of the Infinite: The Pleasures of Mathematics,” Oxford University Press, New York, 2003.

[4] J. W. Dauben, “Georg Cantor: His Mathematics and Philosophy of the Infinite,” Princeton University Press, New Jersey, 1979.

[5] H. Eves, “Foundations and Fundamental Concepts of Mathematics,” PWS-Kent Publishing Company, Boston, 1990.

[6] B. Khumalo, “Revisiting the Derivative: Implications on the Rate of Change Analysis,” 2009. http://www.repec.org./

[7] A. K. Dewdneyy, “Discovering the Truth and Beauty of the Cosmos: A Mathematical Mystery Tour,” John Wiley & Sons, New York, 1999.

[8] All About Science, “Big Bang Theory,” 2009. http://www.allaboutscience.com/

[9] B. Khumalo, “The Concept of the Mathematical Infinity and Economics (Research Note),” International Advances in Research Economics, Vol. 17, No. 4, 2011, pp. 484-485

[10] P. Benacerraf and H. Putnam, “Philosophy of Mathematics: Selected Readings,” Cambridge University Press, New York, 1983.

[11] T. G. Faticoni, “The Mathematics of Infinity: A Guide to Great Ideas,” John Wiley & Sons, New Jersey, 2006.

[12] T. Dantzig, “Number: The Language of Science Pearson Education,” New York, 2005.

[13] C. Zaslavsky, “Africa Counts: Number and Pattern in African Culture,” Lawrence Hill Books, Chicago, 1973.

[14] D. C. Benson, “The Moment of Proof: Mathematical Epiphanies,” Oxford University Press, New York, 1999.

[1] J. Mazur, “Euclid in the Rainforest: Discovering Universal Truth in Logic and Math,” Penguin Books, New York, 2005.

[2] D. J. Struik, “A Concise History of Mathematics,” Dover Publications, New York, 1967.

[3] R. Kaplan and E. Kaplan, “The Art of the Infinite: The Pleasures of Mathematics,” Oxford University Press, New York, 2003.

[4] J. W. Dauben, “Georg Cantor: His Mathematics and Philosophy of the Infinite,” Princeton University Press, New Jersey, 1979.

[5] H. Eves, “Foundations and Fundamental Concepts of Mathematics,” PWS-Kent Publishing Company, Boston, 1990.

[6] B. Khumalo, “Revisiting the Derivative: Implications on the Rate of Change Analysis,” 2009. http://www.repec.org./

[7] A. K. Dewdneyy, “Discovering the Truth and Beauty of the Cosmos: A Mathematical Mystery Tour,” John Wiley & Sons, New York, 1999.

[8] All About Science, “Big Bang Theory,” 2009. http://www.allaboutscience.com/

[9] B. Khumalo, “The Concept of the Mathematical Infinity and Economics (Research Note),” International Advances in Research Economics, Vol. 17, No. 4, 2011, pp. 484-485

[10] P. Benacerraf and H. Putnam, “Philosophy of Mathematics: Selected Readings,” Cambridge University Press, New York, 1983.

[11] T. G. Faticoni, “The Mathematics of Infinity: A Guide to Great Ideas,” John Wiley & Sons, New Jersey, 2006.

[12] T. Dantzig, “Number: The Language of Science Pearson Education,” New York, 2005.

[13] C. Zaslavsky, “Africa Counts: Number and Pattern in African Culture,” Lawrence Hill Books, Chicago, 1973.

[14] D. C. Benson, “The Moment of Proof: Mathematical Epiphanies,” Oxford University Press, New York, 1999.