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.
from A History of Zero
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!