Division by Zero Mathematics Term Paper

Pages: 4 (1382 words)  ·  Bibliography Sources: 4  ·  File: .docx  ·  Level: College Senior  ·  Topic: Education - Mathematics


Also, since any number times zero will equal zero, there is no one unique solution for the answer. Example problems such as 2x0 = 0 and 1450 x 0 = 0 show that a number times zero equals zero. However, at the same time, zero times itself does not equal the number multiplied by zero. The answers cannot be duplicated when the reverse operation is performed (Knifong 1980,-page 179). Even 0 x 0 = 0 is problematic in that zero divided can be divided by itself and multiplied by itself an infinite number of times.

In higher mathematics, such as calculus, the question of division by zero becomes even more complicated. Asymptotes, for example, are lines which correspond to the zeroes of the denominator of a rational function (Kuptsov 2001). This is necessary in determining geometric functions because, since zero can never be in the denominator, the person solving the equation knows that the graph of their equation cannot include the numbers which would allow x to equal zero. For example, if the graph of a line were y = 2/x, x could never be zero because then 2/0 would be an undefined number. The physical presence of x unequal to zero is shown on the graph, but still the solution to a number divided by x is not visible.

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Limits are another component of calculus which complicates the division of a number by zero, but still does not change the fact that it is impossibility. Even in calculus, the actual arithmetic value of zero divided by itself cannot be determined. Instead, the function of the limit is to determine a pattern of mathematical quotients to make a best estimate at what such an answer might be if it were to exist in the real world (Weisstein 2012). The established rule for calculus and limits is that the limit of division by zero can be either plus or minus infinity, or that it can have no limit. This is written as either ? Or -?. With limits, the mathematician can get close to approaching the answer to division by zero; however this is only ever an approximation and is never able to fully solve the problem.

TOPIC: Term Paper on Division by Zero Mathematics Is Assignment

There have been advances in mathematics, such as hypothetical and theoretical math topics, such as fractal Cantonian space time. It is an "operational extension to algebraic groups" which poses that there is a place within quantum physics which would allow for a division by zero (Czajko 2004,-page 261). Researchers in this field have postulated that this division will allow for better understanding and utilizing of "mutually dual line vector spaces" (Czajko 2004,-page 262). Scientific inquiry also poses potential situations where there may in fact be ways to divide by zero. However, it must be noted that all these propositions are theoretical and none have been empirically proven.

In common mathematics, zero is not actually a number. Rather it is the placeholder for the position between positive and negative. It is, in reality, the lack of a number. It cannot be divided because it does not follow the laws and rules of the identities of multiplication or division. A number times zero is zero. However, that zero times itself will not equal the number in the original division problem's numerator. It is because of this inability to conform to mathematical rules that those in the field have labeled the process of dividing by zero as an undefined number, because there is no way to describe it in numerical terms.

Works Cited:

Czajko, J. (2004). On Cantorian spacetime over number systems with division by zero. Chaos,

Solitons and Fractals. (21:2). 261-71.

Fosnot & Dolk (2001). Young Mathematics at Work: Constructing Multiplication and Division.

Heinemann: Portsmouth, NH.

Kaplan, R. (1999). The Nothing That is: a Natural History of Zero. Oxford UP: New York, NY.

Knifong, J. & Burton, G. (1980). Intuitive definitions for division with zero. The Mathematics

Teacher. (73:3). 179-86.

Kuptsov, L.P. (2001). Asymptote. Encyclopedia of Mathematics. Ed. Michael Hazewinkel.


Seife, C. (2000). Zero: The Biography of a Dangerous Idea. Penguin: London, England.

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