Dear Colleague Jack,
This is one great question. Number zero (null) or "0" is essential in math since it is so unique. It represents a strong implication/meaning of the so called "emptiness". Every number multiplied by "0" becomes ZERO. In continuum fulcrum between infinite negative and infinite positive numbers represents MEDIAN value (which shall equally divide both halves). In philosophical and social science terms it borders on "nothingness" since it shows an account balance that is empty of monetary funds, zero profit (break-even, etc.).
Dear Colleague Jack,
This is one great question. Number zero (null) or "0" is essential in math since it is so unique. It represents a strong implication/meaning of the so called "emptiness". Every number multiplied by "0" becomes ZERO. In continuum fulcrum between infinite negative and infinite positive numbers represents MEDIAN value (which shall equally divide both halves). In philosophical and social science terms it borders on "nothingness" since it shows an account balance that is empty of monetary funds, zero profit (break-even, etc.).
Zero depicts an empty set, it is not nothingness. It is the fulcrum between positive and negative. Numbers are relative to each other and part of a scale. take one step forward. Take another step backwards. you are not nowhere, you are in a definable place.
zero degrees Celsius is 273 Kelvin. Is forwards more important than backwards? Is the placement of zero not arbitrary. Yes except for it defines an empty set. A state of affairs, not nothing.
Dear Peter and Derek,
I was not referring to numbers other than ZERO (like 1 or 2). I was just discussing the meaning of ZERO. Mathematicians should also be careful not to overreact, when they attack the notion of "nothingness" ?!? It depends from which angle we look at its meaning ? You are correct, that it can be viewed as not being nothingness, in a division span, between infinite positive and negative. Does it become "nothingness" when you multiply anything by it ? Please tell us what is the monetary meaning of having ZERO balance in your checking account from Managerial, Financial or Accounting perspective ? What is inside "an empty set" ? Why is the set called "empty"? What is inside your special "emptiness" (empty air, or vacuum, wishful thinking or something else) ? Please tell us in philosophical - rational terms, how is "emptiness" different from "nothingness". Please tell us in reasonable, rational terms what is inside your special "emptiness" ? Why does every number multiplied by ZERO becomes "0" ?
Sometimes , we use term of "zero time" in a formulation but are we sure it is really "0" ? maybe it is 0,000......1 and is there a "zero" time(can we stop the time?), or sometimes, we say v=0 are, we sure?
On the other hand 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations? infinity - infinity = 0?
1 + infinity = infinity?
If we use closest number to zero-monad (basic thing that constitutes the universe-everything-)Gottfreid Leibniz, in his essay “Monadology,” suggested that the fundamental unit of all things is the monad. He intended the monad to have some of the attributes of the atom, but with important differences. The monads Leibniz proposed are indivisible, indissoluble, and have no extension or shape, yet from them all things were made. He called them “the true atoms of nature.” At the same time, each monad mirrored the universe.) instead of zero, every equations work I think Science says "Every Thing had originated from a basic thing"
Dear Peter and Derek,
I told you that meaning of "0" can be viewed from multiple perspectives. You and Derek only seem to wish to forward your notion that "0" is in actuallity NEVER ZERO. For bringing something (sheep) and not selling it, you claim that SHEEP still remain. But can you answer my managerial and performance question, being; what did you actualy sell today ? If you and your favorite shepherds sold ZERO sheep, how would smart mathematicians and philosophers measure their performance? What was the purpose of your favored shepherds in coming to the market in the first place? Was it to show off or to actually SELL something? What is the value of what they SOLD, (if, in actuality, they SOLD your favored "Empty set" or wishful "Lala land" ? And, it is curious to state the fact that both of you never answered my question, what is the monetary or financial value of ZERO ("0") balance in your checking or Derek's savings account ? Please tell us academicians what it is, when your purchase at any store or online gets denied due to state of your mighty "empty set" also known as, ZERO BALANCE and what can you mathematicians/ abstraction seekers and philosophers practically do with it ? KR. Dr. Oggi - Management.
Why is the concept of zero so important in mathematics?
Originally Answered:
Quite aside from its practical application, the invention of zero represents an extremely important step in humankind's intellectual evolution. Its adoption by Indian mathematicians in the 7th century allowed the first use of negative numbers and decimal fractions. Zero allowed consideration of maths as a concept as opposed to simply a counting system for tangible or quasi-tangible problems.
By the 12th century, zero allowed the quicker, 'modern' principles of long multiplication and long division to spread to Europe.
The Liber Abaci, written by Leonardo Fibonaci, adopted the numeral during the time of the Christian crusades. Feared by some islamophobes, Florence banned Arabic numerals in 1299. It took another three centuries or so before they finally superseded Roman numerals. It was another two hundred years before negative numbers were accepted because of their association with illegal money lending or usury, a form of blasphemy.
See Alex Bellos' excellent book Alex's Adventures in Numberland.
The opportunity cost of using Roman rather than Arabic numerals would have likely hindered society's development by perhaps several centuries. On that basis, zero has contributed an advancement to science and humanity of a few hundred years.
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Originally Answered:
I wish I could remember all the correct answers to this question. Alas, it has been many years since I studied theoretical mathematics. Perhaps, I can get the ball rolling for those with better memories or more recent exposure to continue.
Zero has two very different uses in mathematics. It serves as a place holder for writing numbers, and it extends the theory of numbers from the natural numbers to integers.
The Arabic system of writing numbers (the one we use) takes advantage of zero to show positions (multipliers) in a large numbers. For example the number 10 has two parts. It has a "1" which is the first counting symbol but it also has a zero which says, in effect, this number is ten times bigger than a simple "1". If we write the number 11 this means one more than 10. The position holding zero has been replaced by a 1 and we know (from elementary school) that means we add both a 1 and a 1 multiplied by ten to get 11. The same trick works for the numbers 100 and 101 except this time the first one is multiplied by a hundred rather than ten. (All of this works because we are using base ten numbers. It would have different values but the same general interpretation if we use a different number base from ten. Alternate number bases popular in the computer world include binary (base 2), Octal (base 8) and hexadecimal (base 16)).
Natural numbers are the kind we use to count things. The first thing we encounter gets represented by the number 1, the second 2, and so on. These are the first numbers to be developed by man and also the first to be developed in theoretical mathematics.
When we start counting backwards using natural numbers we run out of numbers with the number 1. Zero winds up being a good choice for the number that should come after 1 as we count backwards. This can't be done with natural numbers so we invented a new kind of numbers called integers. While natural numbers start with 1 and count upwards to an infinite limit (that is, no limit at all) integers are similar in "Size" but can go in both directions to a positive infinity and also in the reverse direction to a negative infinity. Zero winds up being in the middle and separates 1 and minus-1 (-1). Integers are not necessarily better or worse than natural numbers. Rather, they are a more complicated set of numbers we can use however we wish.
(Just to complete this development, after you get finished playing with integers you can move on to "Real" numbers which include both rational numbers and irrational ones. Both of these new numbers fall in between natural numbers or integers. Rational numbers can be expressed as an integer divided by another integer while irrational ones cannot.)
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Mathematics was actually developed to quantify social variables. And thus ZERO was developed to quantify values like 'nothing', 'none' and so on and so forth.
Apart from that, 0 represents distance distance between an element with itself in a metric space and several other uses defined here:
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Fasten your seatbelts guys. This is gonna be fun.
Forget everything you know from before about this topic. This is how my physics teacher taught in high school.
This is a very important step in learning new things. Curiosity - that's what they call it. Helps you to generate fantastic questions about things we take for granted.
So I did the same thing to our number system.
We have been taught that the number system has 10 digits from 0 to 9.
The first thing which comes to mind is-Why 10?
Well, it could be 11 digits.
I mean, kids could have counted like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, {, 10, 11, 12,…., 1{, 20, etc.
Get it?
In this case prime numbers would be 10 and 12. It would be harder to distinguish between even and odd.
Now coming to the real question, where does zero come into play?
Just imagine you are in search of a number system. The Romans had made one where X is 10. But the problem is with every X they had to add 10. I mean, like XX is 20.
Of course, they had come up with other digits such as L and C. But still they couldn't count exceptionally large numbers.
50 Bucks if someone can write the Avogadro’s number in the comments below in Roman numerals.
Ever heard of exponents? That is the real importance of zero.
We currently have enough symbols to represent numbers as large as Graham’s number as well as decimals for incredibly tiny numbers.
Necessity is the mother of invention.
We needed a new and a better number system. Zero to the rescue. Thank you exponents for saving our precious time or else, we would just write 1 mole as XXXXXXXXXXXXX and a jillion more X’s.
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Catching a glimpse of the history of humanity with respect to Zero is a great way of understanding the latter's importance. The main reason for this is that one can see how difficult everything (from science to building monuments and to shopping in the market) was before this concept was largely accepted.
Therefore, I heartily recommend Charles Seife's excellent book, "Zero: The biography of a dangerous idea", which deals with the exact topic mentioned above. Also, one can learn the disastrous consequences of diving by 0.
By Mara Bruma.
In addition to the beautiful answers, I have a little bit to add:
All responses are concerned with the algebraic point of view.
What about the geometry of ZERO.
Of course, it is not the empty set {phi}.
In general,
we define the point in the space as
" the connected geometrical object of dimension ZERO "
It has no length, no width, and no depth.
The curve has dimension one, the surface has dimension 2 and so on.
ZERO is the whole story, I mean any geometrical object is the collection of the set of points that satisfy certain conditions.
Zero was a great invention in the human history.
Best regards
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