When we worked on the Greek timeline in class, one of the developments in math that really caught my interest was that the Sumerians ‘invented’ zero as a placeholder around 300 B.C., but they did not consider it as a number (http://www.ccsdk12.org/mclemens/Projects/mathhist.htm). I found this fact very interesting because it made me wonder why the Sumerians did not regard zero as a number, and also what practical use for zero they had. Zero has always been such a mysterious number to me, so I decided to do a little digging to find the answers to some of my many questions about the number Zero. Here is what I found:
Zero has many functions in mathematics and number sense. To name a few, the digit “0” is used as a placeholder to distinguish between 1, 10, 100, etc., and it is also used to measure the length of a point and serves as a reference point for distance on a number line. Zero makes it possible for us to subtract a number from itself (ex: 4-4), is the additive identity, and also plays an important role in set theory as it is the cardinality of the empty set (http://www.ams.org/samplings/feature-column/fcarc-india-zero).
Zero was not always considered to be a number as it is today. In the past, Zero was just seen as a placeholder and was not regarded as a true number. There is some debate in the math community about who created zero and when, and the digit appears in writings in many different cultures, namely in the fertile crescent, India, during the time of the ancient Mayans, and also during the time of the Sumerians. It is difficult to really tell when the first zero appeared, because there is not much of a surviving written record, and a lot of math was part of oral tradition (http://yaleglobal.yale.edu/about/zero.jsp). It wasn’t until around 1200 during the time of Fibonacci that Zero became the number we regard it as today.
In class, when we debated what the definition of a number is, many of us considered a number to be a symbol that represents a finite distance from zero. I think that the reason that zero was not so widely accepted as a number in the past because it represented the absence of a number. Numbers were commonly used for measurement or for counting money or possessions (http://www.scientificamerican.com/article/history-of-zero/). How can we measure something or count something that is not there? Zero is the answer. We can count the number of coins we have in our pockets, but we can’t count them if we don’t have any. Since zero is not concrete like the other finite numbers, I think it is the number’s abstract quality that makes us question whether or not it is a true number. I also think that the definition of a number as a measure of distance also extends to zero because zero is also a measure of a distance of zero from itself, and it also describes the distance between every number and itself (ex: 0-0=1-1=2-2=3-3=4-4=…=0), therefore zero is a number.