In the past weeks I paid more attention to the more subtle parts of mathematics while reading. And One of the things that struck me is the number ZERO. There are books where the author mentions that 0 is part of the natural numbers and other books where natural numbers and 0 form the whole numbers. During the book, one needs to pay attention to this thing, because theorems and formulas might have different conclusions with zero. I thought I would search a little about the history of this number.

Although we use zero on a daily basis, few of us ponder its significance. Zero is a vital part of our place-value system. Although this might seem obvious to us now, the theoretical leap required to develop a symbol that represents nothing is very impressive – and neither the ancient Greeks nor the Romans had a representation for zero.

The Indian mathematician Brahmagupta (598 – 670 CE) was the author of the first text to treat zero as a number. It’s sometimes said that you cannot ponder  the infinite until you have pondered zero.[…] the appearance of zero was a huge moment in the history of mathematics.

The history of zero is quite interesting. Even after Brahmagupta used zero as a number, it took a lot of time for the mathematical community to understand zero.

The Indian ideas spread east to China as well as west to the Islamic countries. In 1247 the Chinese mathematician Ch’in Chiu-Shao wrote Mathematical treatise in nine sections which uses the symbol O for zero. A little later, in 1303, Zhu Shijie wrote Jade mirror of the four elements which again uses the symbol O for zero.

In Liber Abaci he described the nine Indian symbols together with the sign 0 for Europeans in around 1200 but it was not widely used for a long time after that. It is significant that Fibonacci is not bold enough to treat 0 in the same way as the other numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 since he speaks of the “sign” zero while the other symbols he speaks of as numbers.

One might have thought that the progress of the number systems in general, and zero in particular, would have been steady from this time on. However, this was far from the case. Cardan solved cubic and quartic equations without using zero. He would have found his work in the 1500’s so much easier if he had had a zero but it was not part of his mathematics. By the 1600’s zero began to come into widespread use but still only after encountering a lot of resistance.

Now, zero is an important number in elementary algebra (addition, subtraction, multiplication, exponentiation). There are quite a lot of rules for dealing with 0, but also a couple which can raise some misunderstandings, one of these is x/0:

In other branches of mathematics, 0 has different meanings and representations. One of my favorite (and the most used in every day life) is in set theory:  0 is the cardinality of the empty set (if one does not have any objects, then one has 0 objects). Also, another interesting one is in propositional logic, where 0 represents the value for false.

I am convinced every one (depending on what part of mathematics they studied more) has a different concept of zero. And it is quite interesting how the philosophical part of it can start quite some interesting discussions. Hope you enjoyed this post, let me know what does “zero” mean for you in the comment box bellow. Thank you for your help and support. You can find me onFacebook,  Tumblr,  Google+,  Twitter,  Instagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!

## 9 thoughts on “Number Zero”

1. Hey, lovely post! My daughter loved the post and wanted to post her own comments. Vakula says – “to me zero means nothing.0 in front of a number has no value.but 0 behind a number can add tens, hundreds even thousands.”

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2. Paul says:

The null set is the set where there is nothing. However when we we wish to enumerate nothing or more exactly the enumerate the place where there is potential for something to exist we need a number, that number is zero.
That number also appears in coordinate geometry as the point 0,0,0 and you can keep going for all of the dimensions, however it is a unit away from -1 or +1 so it actually means it is something. A starting point in counting if you will.
In older telecommunications equipment we often saw a nice number ending in two zeros. The hundred group would be nnnn00-99.
If I say to you have I have a bag with zero apples in it. You can imagine apples, space for apples, however it may contain oranges. It is an absence of something but not necessarily nothing. All fun though.
Null is a vital term in computer databases, it is an absence of a value, however 0 is a value. Maybe computers have poisoned my mind. 😉

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1. Surely computers have not poisoned your mind. 😉 I am quite fascinated about zero and how scientists and mathematicians haven’t actually used it much from the beginning. Recently I have read “Zero: the Biography of Dangerous Ideas” by Charles Seife and it is one of my favorite book so far. It explains why actually people didn’t use Zero that much at the beginning and the philosophical and religious reason behind it. It was quite fascinating for me to find out more about this. I have written a blog post about the book if you want to check it: https://goo.gl/Iou18A

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3. simonwrigby says:

I’ve worked on a lot of ring theory recently, so to me, 0 is the additive identity. In other words, it is the very special and unique element of a ring for which 0 + r = r + 0 = r, for every element r in the ring. Depending on what kind of rings you’re working with, 0 might be the function that is identically zero, or it might be the matrix with zeros in every entry, or it might be the empty set. It might be a totally abstract thing which can’t be described in any other way, except to say that it is “the zero”.

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1. Great, I loved ring theory at university and I think that is the time when I started to be fascinated by Zero. I am actually considering studying Group Theory and Ring Theory a little bit more in my free time because it was my favorite thing in university.
Thanks for sharing your thoughts. Enjoy!

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