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| Yes | 54% | 633 votes |
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Add to FavoritesDivision by zero is done on the Riemann sphere in the complex plane and its result tends to infinity whereas zero divided by any other number tends to one. It is also important to note that in the real number system (and on better graphing calculators), division by zero is not impossible but remains undefined. http://en.wikipedia. org/wiki/Riemann_sph ere
Georg Friedrich Bernhard Riemann, German mathematician, student of Carl Friedrich Gauss, and mathematical genius developed numerous theories in mathematics such as Riemann partitions, The Generalized Riemann Hypothesis, Non-Euclidean Geometry, and extensive work in the realm of imaginary (complex) numbers, and was the mathematician Einstein selected for use in the General Theory of Relativity. Riemann's work in Non-Euclidean geometry just happens to fit exactly with what is actually experienced when taking measurements on the surface of the Earth.
That is, triangles laid upon the surface of the Earth add to 182 degrees instead of the Euclidean 180 degrees. This is due to the failure of the Euclidean fifth axiom, the Parallel Postulate. Its failure is immediately evident to anyone looking at a spherical model of planet Earth where longitude lines at the equator cross at the North Pole proving failure of the parallel postulate (parallel at the equator and crossing at the North Pole). Carl Friedrich Gauss suspected this as well as the existence of non-Euclidean geometry, and the number of primes less than a given magnitude yet did not disclose choosing to let his students discover and receive credit for the items. His most significantly accomplished student was Georg Friedrich Bernhard Riemann.
It is fascinating to note that real numbers generally tend to give imaginary results and imaginary numbers tend to give real results. Meaning that Euclidean results tend to give ideal answers verses real answers and non-Euclidean geometry gives answers consistent with what is really observed in our natural world. This is not to detract from Euclidean mathematics merely that a perfect triangle is merely an idealization and not typically encountered in the real world. Certainly, man can create one but trying to find one in the real world would be as challenging as trying to find a straight line. A straight line laid out on the surface of the Earth would tend to describe a geodesic. Nevertheless, this remains for another topic.
Since the consequences of Riemann's interpretation of non-Euclidean geometry tend to reflect what is actually observed here on Earth, it is tantalizingly imminent that Einstein would indeed use this mathematical model for the description of gravitation. How else could one conceivably proceed? This also provides compelling evidence of Riemann's stature as a founding father of modern physics, a circumstance that will inevitably become more prevalent upon a conclusive solution to the Riemann hypothesis.
In order to provide some degree of logical reasoning for the necessity of division by zero in some (but not all) circumstances, examine the incompleteness theorem presented by Kurt Godel.
"Godel showed that truth cannot be contained within the limits of strict logic. Only if we allow paradox can truth completely reveal itself in form. These two sides of Godel's proof represent the apophatic (via negativa) and cataphatic (via positiva) approaches to truth, respectively. In the apophatic approach, one adheres to strict logic to show that any attempt to represent or speak truth necessarily failsthe truth is beyond all rational comprehension. In the cataphatic approach, on the other hand, one embraces paradox and the coincidence of opposites to demonstrate the tangible presence of truth in all its limitless expressions. Like the ancient mathematics of Pythagoras, Godel's mathematical proof can be seen as a symbol of profound truths about the relationship between the limited and the unlimited, form and formlessness, transcendence and immanence, Godel's postmodern mathematics undermines any attempt to fixate on any totalizing axiomatic system for mathematical discourse, and reveals the essential ambiguity, openness, and emptiness of mathematical activity." Thomas J. McFarlane Spring 2000 Revised and Edited for the Web March 2004.
Inherent to Godel's proof is the conclusion that if a system is consistent, then it is incomplete. Conversely, if a system is complete, then it must be inconsistent. Considering this fact when examining such a precept as the impossibility of division by zero, we would be relegated to an inconsistent mathematics. Alternatively, entertaining the possibility of division by zero generates consistency, yet leaves us with an incomplete understanding of mathematics, which is precisely the circumstance with which we are dealing. Therefore, in some circumstances, one can in fact divide by zero.
http://en.wikip edia.org/wiki/Bernha rd_Riemannnn
http://e n.wikipedia.org/wiki /Riemann_sphere
Mathe matical Poetics of Enlightenment Thomas J. McFarlane Spring 2000, Revised and edited for the web March 2004. http://www.integrals cience.org
Learn more about this author, Darrin A Yarbrough.
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Yes
Division by zero is a violation of the axiomatic system of real numbers. This easily follows from the associative and distributive properties. For example 10/5 = 2 and 2*5 always = 10. If we allowed 1/0 to be defined such that 0(1/0)=1 then we would have to assume that since x/b = y and b*y=x then if we let b = 0 then x = 0(y) even if x were some number other than zero. The number system does not have a rule for this operation, if you use the existing rules it results in a contradiction.
Now, it is not really physically impossible nor is it physically possible to divide by zero. It is simply meaningless. The real number system, which is the environment where actual operations are performed, is an abstraction that does not exist anywhere except in our minds in the same way that there is no such thing as a "dog", that is a set of three letters composed of two constants separated by a vowel which has learned tricks and eats dog food. There are no actual three letters that do tricks and eat dog food, only combinations of letters that we use to convey to one another a representation of such a creature. So it is the same way with the real number system. If we count two apples and one orange we are aware of three fruit, It does not matter how we choose to divide these fruit, there are still two apples and one orange.
Therefore a Division by zero in the real number system is simply an absurdity according to how our system for processing numbers has been defined and division by zero in physical reality is also meaningless because we do not perform any mathematical operations on the material world anyway.
You may be thinking, I perform mathematical operations, I count beans, if I miscount the beans then I must either add beans or subtract beans until the count is correct. OK then, you count beans, you add beans, you subtract beans. But the beans don't care. If you count the beans wrong, then count them wrong again, and keep counting them wrong, the beans are unaffected. The number of beans that are out there does not change as a result of your count. You could get fired from your bean counting job and the beans won't miss you. If they can't find a new bean counter to replace you, the beans will still be beans and are not affected by whether they get counted or not.
Even if you correctly guess the spin of a photon, it doesn't mean you cannot correctly guess the position of the photon. You knowing the angular velocity and the position of the photon are not physically mutually exclusive. Your measurement of its position screwed up your ability to know its velocity because your system of measurement is inadequate. You are not changing the photon by cognate recognition but rather by physical scale limitations. This is no major revelation and the same could be said of performing any mathematical operation in the physical universe. Not only is division by 0 physically meaningless but so is multiplication and division by 10.
Learn more about this author, Mike Mueller.
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