What is the origin of zero and how do we explain it to layman?. Can we add/delete some more surprising properties to zero. Are there several types of zero like infinity? What price to pay for excluding zero from real number system like infinity? What are the other possibilities to define zero?
This article "A history of Zero" is very good reading! Many historical facts on ZERO!
This book "The Nothing that Is: A Natural History of Zero" by Robert Kaplan seems a good book regarding this issue!
http://www.amazon.com/The-Nothing-that-Is-Natural/dp/0195142373
It is said that in the "Aryabhatta and origin of zero". in one of my earlier Q&A answers on numbers, I got a negative vote, hence i stopped with it... Anyhow, i am now enclosing a link...
http://incredblindia.blogspot.in/2009/02/aryabhatta-and-evolution-of-zero.html
Dear Shafig, thank you for scientific American reference. These lines are also from the same link:
"There are at least two discoveries, or inventions, of zero," says Charles Seife, author of Zero: The Biography of a Dangerous Idea (Viking, 2000). "The one that we got the zero from came from the Fertile Crescent." It first came to be between 400 and 300 B.C. in Babylon, Seife says, before developing in India, wending its way through northern Africa and, in Fibonacci's hands, crossing into Europe via Italy.
It seems that opinions are devided on this matter. which one to believe?
It seems that in ancient Egypt the number and numeral zero have been appear. For history see: http://en.wikipedia.org/wiki/0_(number)
Zero is the neutral element of the ring Z of integers, the field of rational numbers, and the field of real numbers.
As these number systems get a lot of generalisations, the same holds true for the meaning of zero. The most characteristic is the Robinson’s Nonstandard Analysis. There the standard zero comes with a “cloud” of infinitesimals around it. If εis an infinitesimal then 1/ε is an infinitely large number, bigger than any standard real!
There are many other models, e.g. Boolean0valued models in which the number zero plays a role of a “random variable” or a “self adjoins operator” depending on the Boolean algebra we use. The Cantor ordinal and cardinal numbers cannot be used to get an infinitesimal as their inverse.
'Zero' implies 'absence', and therefore the logical consequence of presence and counting or not? Why mathematicians added a 'zero' to '1' to form '10'? Why not 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, .... Did the 10 fingers of the two hands of a person counting with fingers provided inspiration to produce '10' following '9' in stead of '11' following '9'?
For the concept and expression of 'zero' in Ancient Egypt, you can read a good article by J. Winand at the journal 'Lingua Aegyptia' published in 2009: http://wwwuser.gwdg.de/~lingaeg/lingaeg17.htm
I hope this can help you
Regards
This is taken from google book page about the following book: Seife, C. (2000). Zero: The Biography of a Dangerous Idea: Viking. I have not read the book.
The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Seife, a US correspondent for the international magazine New Scientist, follows the number zero from its birth.
http://books.google.com/books?id=f7_aAAAAMAAJ&q=zero&dq=zero&hl=en&sa=X&ei=eai7U8DwMOet0QWfmYC4Cw&ved=0CB4Q6AEwAA
The first recorded zero is attributed to the Babylonians in the 3rd century BC. A long period followed when no one else used a zero place holder. But then the Mayans, halfway around the world in Central America, independently invented zero in the fourth century CE. The final independent invention of zero in India was long debated by scholars, but seems to be set around the middle of the fifth century. It spread to Cambodia around the end of the 7th century. From India it moved into China and then to the Islamic countries. Zero finally reached western Europe in the 12th century.
Zero was invented independently by the Babylonians, Mayans and Indians (although some researchers say the Indian number system was influenced by the Babylonians). The Babylonians got their number system from the Sumerians, the first people in the world to develop a counting system. Developed 4,000 to 5,000 years ago, the Sumerian system was positional — the value of a symbol depended on its position relative to other symbols. Robert Kaplan, author of "The Nothing That Is: A Natural History of Zero," suggests that an ancestor to the placeholder zero may have been a pair of angled wedges used to represent an empty number column. However, Charles Seife, author of "Zero: The Biography of a Dangerous Idea," disagrees that the wedges represented a placeholder.
The concept of zero first appeared in India around A.D. 458. Mathematical equations were spelled out or spoken in poetry or chants rather than symbols. Different words symbolized zero, or nothing, such as "void," "sky" or "space." In 628, a Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero — a dot underneath numbers. He also developed mathematical operations using zero, wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. This was the first time in the world that zero was recognized as a number of its own, as both an idea and a symbol.
Over the next few centuries, the concept of zero caught on in China and the Middle East. According to Nils-Bertil Wallin of YaleGlobal, by A.D. 773, zero reached Baghdad where it became part of the Arabic number system, which is based upon the Indian system. Cartesian coordinate system and in Sir Isaac Newton’s and Gottfried Wilhem Liebniz’s developments of calculus. Calculus paved the way for physics, engineering, computers, and much of financial and economic theory.
The Sumerians’ sy
This article "A history of Zero" is very good reading! Many historical facts on ZERO!
This book "The Nothing that Is: A Natural History of Zero" by Robert Kaplan seems a good book regarding this issue!
http://www.amazon.com/The-Nothing-that-Is-Natural/dp/0195142373
Dear Kamal,
it does not matter if it ends at zero or at a natural number n
Dear all,
I am thankful for your valuable contribution on "0". But most of the discussion has been focused on to history of origin of "0". What about future of "0"? I mean; Can we add/delete some more surprising properties to "0". Are there several types of zero like infinity? What price to pay for excluding zero from real number system like infinity? What are the other possibilities to define zero?
Ismat
About the relationship between Mathematics and Nature:
Does 'zero=absence' truly exist in nature? Does 'zero=absence' result from biology-based human perception constraints? At any place in universe there is at least something although most of not not perceived by humans, or not?
Zero by itself may not a value; but upon combination after a digit or so, its value is truly manifested... In our tradition it is said that during marriages the elders used to bless the newly wedded couples.... "as individuals you both had UNIT values, but now on your inert existence would change to more powerful values .... when one person takes a lead other person should be a zero to add value.... such a give and take would take things much farther in life...."
So being a 'zero' has symbolic value in communication and may upgrade relatives or colleagues from a social point of view.
Can we find "zero" in nature? Well, let us take the surface of sea. Then measuring hight, is a real number and measuring deepness is denoted as a negative number. With a little abstraction, this is an example of zero in nature+mind
From a Psychology point of view, is it important to play 'zero' to motive colleagues?
ZERO is the loop that binds all numbers and state at the same time links all values by empowering them into meaningful quantity; thereof impossible to completely be eliminated. Quantisation Approach as applied to absolute darkness and/or absolute brightness in comparison to/with pair of particle basis. One can argue that the concepts are laced with unpredictability in a physical state and/or system therefor phenomenon yet fully understood. (Dr Bonny B. N. Umeadi)
I agree with Ismat. ZERO is the loop that binds all numbers and state at the same time links all values by empowering them into meaningful quantity.
You are right Mr Mahfuz Judeh, “ZERO is the loop that binds all numbers and state at the same time links all values by empowering them into meaningful quantity (Umeadi 2007). That is my work still developing into different facets, as applied to Nano/Micro sensor technologies; for now to monitor Oil and gas pipeline system.
Dear @Boniface,could you attach your paper of 2007, I could not find it at Research Gate! Thanking You in advance!
it is part of on going patent for our sensors, hence not make public yet.
it is part of on going patent for our sensors, hence not "made" public yet. "Quantisation and information relay process"
Dear Ugur,
Thank you for so much for your intriguing and illuminating answer. I fully concur with you! You have summarized and unfolded the philosophical history that underlies an idea of Indian origin.
Yale Global Online
http://yaleglobal.yale.edu/about/zero.jsp
The history of zero
Nils-Bertil Wallin
YaleGlobal, 19 November 2002
@Costas Drossos: Can we find "zero" in nature? Well, let us take the surface of sea. Then measuring hight, is a real number and measuring deepness is denoted as a negative number. With a little abstraction, this is an example of zero in nature+mind.
Great example, dear Costas! Your example might be called "vertical zero" in nature. Here is an example of what can be called "horizontal zero" in nature, thanks to agreements about the division of land between countries.
Consider, for example, the land in southern Albania and the land in northern Greece. To the north of Greece, we have positive distances from the border of Greece into Albania. And to the south of Albania, we have negative of distances from the border of Albania into Greece. This suggests that there are many natural horizontal zeros in nature.
Yes dear @James, very good examples of "ZERO" in nature! Both, vertical and horizontal zeroes in nature!
What do You think about this quote that I have found on Math Forum! The question was "What is natural Zero"?
One of the answers follows: "Natural zero basically means "There isn't any...
E.g. Height, Weight have a natural zero because you could say "there isn't any height, there isn't any weight, etc."
If "zero" is taken to mean something else besides "there isn't any", then it is not a natural zero.
E.g. Years - Year 0 is an arbitrary point in time, and it is so named because it was convenient to use the year Christ was born as a zero.
Temperature - 0o C is an arbitrary temperature, and it is so named because it was convenient to use the freezing point of water as a zero." "!
http://mathhelpforum.com/statistics/123532-what-natural-zero-used-ratio-scale.html
The comments from the Math Forum, dear @Ljubomir, take us in an interesting direction. Just a little rewriting is needed to extract natural zeros from the examples.
Instead of thinking of a natural zero as "there isn't any", it makes more sense to think in terms of a natural zero as the starting point of something. For example, zero degrees Celsius is the starting point of positive temperatures. Or, if we include negative temperatures, then a natural zero on a temperature scale is that point between negative and positive temperatures. I think this is basically what dear Costas Drossos was saying with the example of natural zero being that point between below the surface of the earth and above the earth's surface.
Dear All;
Please also read and comment on the other part ; Can we add/delete some more surprising properties to zero. Are there several types of zero like infinity? What price to pay for excluding zero from real number system like infinity? What are the other possibilities to define zero?
Zero is a point in the real line R. If we take the ultrapower of R, *R, then zero in R, carries with it a monad of infinitesimals, which constitute a subring of *R. Thus all these infinitesimals cannot be seen when we view R with naked eye. So in this way they are hidden zero's! 1/ε where ε is an infinitesimal, defines an infinitely large number, different from cardinals and ordinals of Cantor.
In addition there are infinitely many models of first order properties of real line. In each of these models we have different types of zero!
Difficult to attain, Sustainable and environmental Zeros! ( Zero carbon and Zero net energy houses)
http://www.treehugger.com/sustainable-product-design/ruralzed-uks-first-commercially-viable-zero-carbon-home.html
http://www.treehugger.com/green-architecture/nist-net-zero-energy-house-fact-net-positive-it-still-robotic-green-dinosaur.html
Shall I compound the notion: Space or Zero often coexist in lineal thinking. Take information relayed (outward) that processing of information often follow known cycles (invocation or knocking) step-by-step progression, zeroing to space where a response to a step must be elicited before another (data –Forward or Backward) step is taken. Often systems have in centuries been designed based on responding to one stimulus before responding to the next. Egyptian applied the Zero many years before the Indians based on logical and orderly placement of numbers mathematically and scientifically. However; the construction of fuzzy logic (not being an expert but avid applicator) is based on Nonlinear thinking that is more abstract; what I referred often as: magnetic field boundary at any given point is specified by both a direction; that starts at a positive electric charge and ends at a negative electric charge; other possibilities to define zero.
Zero can be viewed as a pressure point in mathematics, i.e., a starting point for lots of interesting (possibly new) interpretations of 0 and its various roles.
One promising place to look for new interpretations of zero is in terms of vector spaces.
A vector is an element of a vector space such an n-dimensional Euclidean space. A vector is represented by a list of numbers called the components of the vector. A vector space is a set of vectors that is closed under vector addition and multiplication. Every vector has a tail (its beginning) and a head (its tip or end).
http://mathworld.wolfram.com/Vector.html
A zero vector (denoted by a boldface 0) is a vector of length and all of the components of a zero vector are zero. A zero vector is the additive identity of the additive group of vectors. For a picture of a zero rector, just imagine a point. This means that zero vector has a tail that equals its head.
http://mathworld.wolfram.com/ZeroVector.html
Zero can be viewed dear friends in a the uncountable way, as we, the mathematicians and the math applicators (read engineers...) are full of new ideas, it is just a matter of time!
Zero and set theory
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.
http://en.wikipedia.org/wiki/Empty_set
Dear Ljubomir,
You got me! What is this "in a the uncountable way"? Do you mean zoro asa menber of R?
I have got You dear @Costas, you could consider 0 as member of R with no value! Is that what You were trying to point out?
This discussion is turning out to be very interesting!
Dear Behrouz, Ljubmir and Costas, have you considered the idea of an empty vector? In a real vector space, I believe an empty vector is identfied with the zero vector. This makes sense, since the zero vector has no length or rather has zero length.
Dear @Costas, our friend @James gave an extra fine example of what I have meant! :)
zero,zee-row,z-ero
significance of zero we will realize only then,
how many zero's i am writing in-front of 1(one)
zero diya mere bharat ne
india gave zero at the time when it was difficult to measure the distance between land and moon Arya bhat
Thanks to all the contributors
Three new infinitude related number forms were discovered: inter-small, indistinct-small; inter-great, indistinct-great; yan. And a new number spectrum was constructed: zero, infinitesimal, indistinct-small, finite-number,indistinct-great, infinity, yan.
The discovery of yan makes up the meaning of zero and making perfect the theory of zero as well as the theory of “big” and “small”. The definition of zero is “absolute nil” while the definition of yan is “absolute existing”. These are a pair of concepts nothing to do with numerical “more, less, big, small”: a pair of special number forms without the meaning of “big” and “small” themselves but express the meanings of “number” ,“value”, “big” and “small”. There is no absolute “more, less, big, small”, but only specified “more, less, big, small” within the domain of specified zero and yan in our science. So, theoretically, zero is not “very small number” and yan is not “very big number”; but practically within the domain of specified zero and yan, a “very small number” can be a zero while a “very big number” can be a yan. Thus in applied mathematics and applied infinitude, we can have specified “more, less, big, small” number within the domain of specified zero and yan in the cognizing process to the infinitude related mathematical things through the indistinct-number cognizing and treating theories and techniques（such as limit theory）. Our science history with zero, fuzzy number and approximate number proved that our mathematics cannot be without either zero or yan.
ZERO does not mean only a numerical value but also to start afresh.
Origin of Year 0 and AD, BC
Monk Dionysius Exiguus in 6th century and more commonly adopted in the 9th century, was the one who initiated the modern system of counting the years. Prior to that, according to the biblically-calculated time since Adam, or Anno Mundi (AM), Christianity counted years by the reign of the Roman emperor. The AM count was based upon biblical passages. In particular, it used a 12 hour analogy, with Jesus appearing at the 11th hour. Dionysius proposed an alternative calendar that set the year 0 to Christ's incarnation upon the world based upon the history available to him, and to the beginning of the age of Pisces (where new years began with the sun in the constellation of Pisces). Pisces, the sign of the fish, was linked to the first Christian symbol, ICHTHYS (i.e., fish in Latinised Greek).
http://www.calendar-origins.com/calendar-origins.html
Let have some humorist answer! The origin of zero is just a point on the axis!
In mathematics, we need to study 2 natures of zero: the existing meaning and numerical meaning, so we may have both “theoretical zero” and “applied zero”.
Here are a couple of forms of zero that may interest the followers of this thread:
> Approximate zero: An initial point that provides safe convergence of Newton's method. Applying Newton's method to the roots of any polynomial of degree two or higher yields a rational map of , and the Julia set of this map is a fractal whenever there are three or more distinct roots. Coloring the basin of attraction (the set of initial points that converge to the same root) for each root a different color then gives the attached set of plots.
http://mathworld.wolfram.com/NewtonsMethod.html
> Division by zero. Defined, for example, for limits such as lim x-->0 sin x / x and
lim x--->o+ 1/x.
http://mathworld.wolfram.com/DivisionbyZero.html
“Applied zero” has much to do with infinitude------in analysis theory, set theory… but most terrible thing is in infinitude related paradoxes.
This continues to be a very good question, with lots of twists and turns in the ongoing dialogue.
Dear Geng,
Yes, the seeming infinitude of paradoxes related to zero is a bit daunting. The idea of zero has lots of interesting philosophic nuances, starting with the fact that scientists shy away from zero in their measurements. The whole idea with measurement is to have some to measure. And having nothing to measure (a zero quantity) defies our intuition. And yet zero is an essential stopping point (if we are counting down). A paradox occurs when we are looking for small quantities (with small measurements) but not zero quantities.
Cauchy was especially gifted in his use of zero in, for example, the limit of a sequence of a monotone decreasing function or in defining the integral in terms of limits. It was Leibniz who let a zero difference be in the denominator in working with differentials.
More recently, there has been considerable work on contraction mappings (shrinking distance functions). Perhaps Prof. Beg can comment on the possibility of a contraction mapping where the distance shrinks to zero.
You are right that a paradox occurs when we are looking for small quantities (those infinitude relating mathematical number forms). But more terrible things happen according to my studies that any non-limit-getting “y ------>0 infinitude things” treating cases in our present mathematics are all family members of Zeno’s Paradox-------plenty of. Cauchy was really especially gifted but the pity is his work (any theory in present mathematics) can never solve Zeno’s Paradox.
Dear Geng,
I looked at you paper ICM, 2014, and I really do not understand anything!
To see the real value of your papers, please sent at least one not to
“Journal of Kashgar Teachers’ College”, but to an respected one, and see their remarks. My opinion is that your paper, either it is not well written, or there is no clear proof of anything! Sorry about that, but I must express what are my impressions.
Dear Costas，
My heartfelt thanks to your frankness, but I am sorry to tell the truth that no respected journal can accept my paper so far because of so much anti-tradition. Well, I act but God decides.
But if possible, would you please be so kind enough as to let me know exactly “either it is not well written, or there is no clear proof”.
Best Regards
Can we use the “brackets-placing rule"(１＋1/2 ＋（1/3＋1/4 ）＋（1/5＋1/6＋1/7＋1/8）＋．．．) applied in the divergent proof of Harmonious Series (1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．．) to produce infinite numbers bigger than 1/2 or 1 or 2 or 3 or 4…?
This is not my idea. Please see following proof:
1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．． （1）
=１＋1/2 ＋（1/3＋1/4 ）＋（1/5＋1/6＋1/7＋1/8）＋．．． （２）
>1+ 1/2 ＋( 1/4＋1/4 )+（1/8＋1/8＋1/8＋1/8）＋．．． （3）
=1+ 1/2 + 1/2 + 1/2 + 1/2 + ．．．------>infinity （4）
Such an antique proof (given by Oresme in about 1360), though very elementary, can still be found in many current higher mathematical books written in all kinds of languages. And this proof has been acting as a basic theory of mathematics producing many mathematical conclusions.
But the problem is we meet a modern version of “Achilles and Tortoise” Zeno’s Paradox------- Harmonious Series Paradox: the runner in Zeno’s Paradox is exactly that of “brackets-placing rule", while the tortoise’s walk is exactly those items in harmonious series. Although the runner can run very fast, the tortoise is surely in front of him theoretically --------although the “brackets-placing rule" uses up plenty of items in the infinite harmonious series, there still be unlimited items in the infinite harmonious series awaiting to be produced into any numbers theoretically. So, not matter how fast the runner can ran, he will never catch up with the tortoise in Zeno’s Paradox while the “brackets-placing rule" in Harmonious Series Paradox can produce infinite numbers bigger than 1/2 or 1 or 100 or 100000 or 10000000000 or…!
Our system for representing numbers has its roots in the system used by the Babylonians about 4000 years ago. Their system was base 60, or perhaps a combination of base 60 and base 10, and was a positional or place-value system, that is, the relative position of a digit enters into determining its value. In our system we multiply by successive powers of 10 as we move to the left - the Babylonian used powers of 60.
The Babylonian system was ambiguous though because it lacked a symbol for 0. Occasionally a space was used to mark a missing digit, but trailing spaces were not used (and would be difficult to detect). In addition multiple successive spaces would be difficult to detect accurately. The Babylonians relied on context to resolve the ambiguity.
In a later period, 600 BC to 300 AD, a symbol for zero was introduced, but it was not used as a trailing zero. Thus one could not really distinguish 3600, 60, 1, 1/60, and so on, except by relying on the context.
The Egyptians, around 1650 BC and earlier developed a base 10 system, but it was nonpositional. One can view such a system as additive. For example, if "1" is the symbol for one and "A" is the symbol for ten, then twelve can in principle be written as 11A, A11 or 1A1. Of course the Egyptians did have a preferred order for writing their symbols
http://people.oregonstate.edu/~peterseb/misc/sonja_dots.html
Dear Kamal,
I am confused by your statement! Please give me your light to understand what is the value of zero from left or right? It is not only that, there are 8 RGers who find your answer interesting. It seems that the only one who does not understand is me, a mathematician!
Actually our operation in Harmonious Series Paradox is: to change an infinitely decreasing Harmonious Series with the property of Un--->0 into any infinite constant series with the property of Un--->constant or any infinitely increasing series with the property of Un--->infinity--------this means that not matter what kind of runner (even a runner with the speed of modern jet plane) held the race with the tortoise in Zeno’s Paradox, the runner will never catch up with it.
“Achilles and Tortoise” Zeno’s Paradox has disclosed the "real infinite--potential infinite" fundamental defects in present traditional infinite related science theory system. In this theory system, the critical defects are unsolvable because we are not allowed to forget either "real infinite" or "potential infinite" in such paradox (exactly same situation happen in Harmonious Series Paradox).
That is why this paradox family has been troubling us human for more than 2500 years.
Origin of Zero and the Decimal System
The zero was known to the ancient Indians and most probably the knowledge of it spread from India to other cultures. Brahmagupta (598-668),who had worked on mathematics and astronomy, was the head of the astronomy observatory in Ujjain, which was at that point of time, the foremost mathematical centre in India; he and Bhaskar the second (1114-1185), who reached understanding on the number systems and solving equations, have together provided many rules for arithmetical operations with the zero.
Varahamihira (505-668) who was educated in Kapitthaka and was one of the patrons of the school of mathematics in Ujjain, worked on Hindu astronomy before Aryabhata.He wrote manuals called Panchasiddhantika which refer to the addition and subtraction of zero.
Vasubhandu (around 400 AD), who was born into a Hindu family but later converted to Buddhism, expressed his belief that the stars were representative of the zero and placed there by the Creator to remind humankind of the transience of the world and all beings. The symbols for nine numerals and a symbol for zero were well-established by the fifth century AD.
http://www.indiaheritage.org/science/math.htm
Salaam & kind greetings to all.
For the last few years I have been receiving notes and "announcements" from my good highly respected friend Saburo Saitoh regarding division by Zeo. Yesterday I distributed his attached "Announcement 185" to my email list addressees upon his request. I thought attaching it here may enrich the onversation further and contribute to the communications at hand by default. For months now I have been promising Saitoh a serious focussed piece of my mind regarding his/and colleagues advanced theories in the annoucements and his references, and perhaps having dried up-hopefully temporarily- of intelligent things to say (depending on the conversations I can perhaps dig up the things I already written in previous emails to Saitoh for sahring here), I am sort of laying this heavy obligations on you my dear RGers.
I urge the readers to look at the references as well to get acquainted with Saitoh's position on this matter. I have shared some of my disposition thoughts and criticisms few times in person, but perhaps it is for some of you dear RGers to contribute through this question.
Please feel free to communicate with Saburo Saitoh through this email as well:
- Saburou Saitoh
- In case you send emails to Saqitoh regarding this issue, I would appreciate a CC.
Kindest regards,
FBMB. ([email protected]).
Thanks dear @S. Saitoh for Announcement 185: The importance of the division by zero z/0 = 0. It is fine contribution to this thread! "The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by the method of Michiwaki in the elementary school, even..."
I think that discussion will be enriched, let us see!
If I remember correctly, once Albert Einstein thanked India for contributing zero to number system. As an Indian, I always enjoy this compliment of one of the greatest ever.
When we talk about “the origin of zero" we can not avoid “the meaning of zero".
But when we study ”the meaning of zero" and the location of zero in “number spectrum” in our mathematics, an unbalanced defect can be easily discovered: “zero" appears on one side of the “number spectrum” as a kind of mathematical language telling people a situation of “ nothing, not-being,…”; but on the other side of the “number spectrum” we lack of another kind of mathematical language telling people an opposite situation to “zero”------“ something, being,…”.
We need a new number symbol (“yan”) with opposite meaning to zero locating at the opposite side of zero in the “number spectrum” to make up the structural incompleteness of “number spectrum” and to complete the existence of “zero”.
As a kind of mathematical language, can zero be illustrated by following “zero tree” through out our mathematics history.
(1) a kind of reference ------- generator, middle, neutral, beginner, origin, placeholder, marker,…,
(2) absolutely non-existent ------- without numerical value meaning, the negation of being, objectively nothingness,
(3) relatively non-existent ------- with numerical value meaning, subjectively nothingness, the approximate nothingness, the result of infinitesimal limit , ….
Dear Mr. S. Saitoh
What do you think of above “zero tree”? I think the 0 in that paper of announcement 185 belongs to the category 2 in that “zero tree”.
My regards to you, Geng
Dear Mr. S. Saitoh
Thank you for your references paper.
Sincerely yours, Geng
Dear Mr. S. Saitoh ，
What kind of property do you think 0 has in 100/0=0?
So, would you share with us what 0 is you think?
Sincerely yours, Geng
Dear Mr. S. Saitoh
Zero is really an important mathematical language for us to study and understand.
My regards to you, Geng
One thing has been troubling many people for long: at the time when 0 was born as a kind of number in our science, must it be proved mathematically or just came out as needed and staying there without proof?
Dear: All
For me, zero is so important, because it;s interpret the starting point.......!
We can know and measure by calibrating it from zero..............;)
We human need zero so we create zero without any mathematical proofs, which is the way we create number forms. We need this kind of number form, so it is there in our science. Is this the origin of "zero"?
Dear All
I get another point, that zero is the benchmark scale points.......
"From placeholder to the driver of calculus, zero has crossed the greatest minds and most diverse borders since it was born many centuries ago. Today, zero is perhaps the most pervasive global symbol known. In the story of zero, something can be made out of nothing" - Nils-Bertil Wallin.
For more details see http://yaleglobal.yale.edu/about/zero.jsp
Dear Ismat Beg,
I find interesting article and sent you.
http://www.scientificamerican.com/article/history-of-zero/
Regards, Shafagat
The origin of zero is a big successful step in our cognitive ability in numerical field-------from the view point of “number spectrum” to quantitatively cognizing universe.
Making better “number spectrum” (with infinite related numbers included) will be another big successful step in our cognitive ability in numerical field for quantitatively cognizing universe.
This work is on the way now.
Contribution from Smithsonian museum: The Origin of the Number Zero!
"Deep in the jungle, an intrepid scholar locates a symbol of power and mystery...
Four miles from the great temple of Angkor Wat, deep in the Cambodian jungle, I opened the door of a makeshift shed with a corrugated tin roof and walked into a dusty room painted in pale gray. Thousands of chunks and slabs of stone covered the dirt floor: smashed heads of statues of Khmer kings and Hindu gods, broken lintels and door frames from abandoned temples, the remains of steles with ancient writing. After years of searching, I’d finally arrived here, hoping to find a single dot chiseled into a reddish stone, a humble mark of incredible importance, a symbol that would become the very foundation of our number system—our first zero..."
http://www.smithsonianmag.com/history/origin-number-zero-180953392/?no-ist
The indian mathematicians discover 0 to mean nothing. Later the muslim mathematicians use zero to fill the empty digit in numbers.
I recently received the attached files and the kind and informative message below (dated : Dec-27-2015) from Prof. Saburo Saitoh, regarding the "Division" by Zero.
and I replied this morning with this message
Dear Prof. Saburo Saitoh,
Kind greetings and happy new year, to you and yours!.
Thank you for sharing, as always, and thank you for your kindness.
I am happy and eager to read of your continued achievements in the subject of the attached papers, stepwise.
If I may share few things about this issue in addition to what I wrote you before in email and in ResearchGate (regarding origin of Zero), where you recall, I invoked your work regarding the division by Zero, here:
https://www.researchgate.net/post/What_is_the_origin_of_zero
1. As you well know Zero is NOT a Natural Number like 1, 2 or 3. That is Zero is the "lack of numbers" so to speak, just like the empty set represents the lack of objects, and dark represents the lack of light, and "the color" black represents lack of color...!
2. In Physics they speak of matter and anti-matter (dark matter) or black holes "matter" (which absorbs all matter and even light cannot escape...etc) similarly Zero absorbs eveything multiplied with it.
3. So in a sense, in an analogous fashion, multiplication with Zero, and consequently the division by Zero may be inherently as special as when the Anti-matter deals with matter, perhaps.
4. I will even say that if 1, 2, 3 ...etc are YANG, then Zero is probably YING...
So that if the natural numbers give rise to some exciting mathematics , so does the study of Zero (and the division related you are studying) give rise to a different, but equally exciting mathematics.
5. We have many examples of this in mathematics where one instance is equivalent to the rest in terms of importance and intricacies, just like, if the integration of x^n (n=-1) gives rise to logarithms (and hence exponentials and transcedental functions mathematics), versus the integration of x^n (n different from -1) giving rise to polynomials related mathematics.
6. My Current Belief/Conclusion is : "the division" by Zero is not a single answer, but a multitude of answers depending on a case by case basis (or approach just like in the limits). In fact, it better be not be one single answer, otherwise in my personal sense, all Mathematics in particular, Arithmetic and Algebra, as we know them will be in trouble.
I believe we have to redefine the operation "Division" when we deal with Zero.
7. I admit that there may be a system of conditions or rules, where,
1/Zero Turns out to be Zero, (*)
nevertheless, this cannot be every time and under any circumstances (Turns out to be versus = equal, NOT THE SAME) .
8. As this depends on the way we reached to this equation (*) and in what context, as this Division is NOT a Natural Operation, in the sense that Division by any other Non-Zero number A ( 1/A), is.
9. So to try to make sense of (*), in the same sense of division by say a Natural number ad within the same rules, may be rather un-Natural. So what is needed is simply a separate set of definitions and Game Rules, and hence hopefully new (but must be Robust) Mathematics.
10. and like we say in our culture, God, the Creator Knows Best!.
Kindest regards,
FBMB.
PS: This message including yours below and the attached files, is being bcced to my associate colleagues for the benefit of sharing, and for the purpose that your premise and diligent work is seen more widely. I expect and hope you that you end up receiving direct independent input from my recipient colleagues, regarding your work.
---------- Forwarded message ----------
From: Saburou Saitoh
Date: Sun, Dec 27, 2015 at 11:34 PM
Subject: Re: http://www.fractalsciencekit.com/tutorial/examples/examples.htm
To: "Dr. Fethi Bin Muhammad Belgacem"
Dear Professor Belgacem:
Thank you for your kind Greetings.
Hope A Happy New Year
The division by zero 1/0=0 is clear and trivial, we found many evidences and we will be able to see a new world.
Please look the attached evidences.
With best regards,
Sincerely yours,
Saburou Saitoh
2015.12.28.5:35
2015-12-28 3:11 GMT+09:00 Dr. Fethi Bin Muhammad Belgacem :
Dear Colleagues,
Salaam and Happy Holidays!
FYIC!: Find Fractals Sciences Kit here:
http://www.fractalsciencekit.com/tutorial/examples/examples.htm
Kindest regards,
FBMB.
--
Coordinates:
Fethi Bin Muhammad Belgacem,
Department of Mathematics,
Faculty of Basic Education,
PAAET, Al-Ardhiya, Kuwait.
Mobile: (+965)-9985-2474
Secondary Email: [email protected]
SCOPUS IDs: 6504575250 & 16641829200.
ORCID: 0000-0003-0228-7829; MRAID:679116.
GS: https://scholar.google.com/citations?user=ZX_MO_QAAAAJ&hl=en
RG: https://www.researchgate.net/profile/Fethi_Belgacem/?ev=hdr_xprf
- Badges
- Science topic
- Similar topics
- Mathematics