What If There Was No Zero?
Date: 10/21/2003 at 07:18:33 From: Melissa Subject: the importance of zero If the zero is so important, why did it take so long to be discovered? Why did some civilisations just not need to have a zero? And also, could you please give me some examples of what we can now do in maths that we wouldn't be able to do if we didn't have the zero? If we had never discovered the zero, what sort of maths wouldn't we be able to do? Where would maths stop? I cannot imagine maths without zero! I had to do a project on the history of the zero.... and as I was presenting it, I was really trying to find an answer to those questions, but I never did!
Date: 10/21/2003 at 12:43:30 From: Doctor Peterson Subject: Re: the importance of zero Hi, Melissa. I think that without the concept of zero (and negative numbers, which go with it, and may even have led to its full acceptance), algebra would have stagnated at about the stage it reached around 800 AD. The problem is that many things we do in algebra either require zero in order to be expressed neatly (such as inverse operations), or would have to be done in several separate cases according to whether some variable or coefficient was positive, negative, or zero. Including these numbers unifies everything and makes it possible to do much more in a single solution. Without them, much of algebra, calculus, and beyond would have remained too difficult to learn, apply, and build on. Yet until you get to algebra, there is really no need for zero! It helps as a digit in our number system, but earlier number systems did fine without it, because they were not used for anything but counting and measuring real objects, using positive numbers. It is only when you want to extend the reach of numbers, and start using variables, that you find zero and negative numbers necessary. Here are a few discussions of the history of zero from our site (and one favorite link) that will help answer your questions: A History of Zero http://www-history.mcs.st-and.ac.uk/HistTopics/Zero.html Why is Zero Not a Natural Number? http://mathforum.org/library/drmath/view/57186.html Purpose of Zero http://mathforum.org/library/drmath/view/57051.html History of Zero and Place Value http://mathforum.org/library/drmath/view/52566.html Year 0 http://mathforum.org/library/drmath/view/52475.html Zero for Children http://mathforum.org/library/drmath/view/58763.html Practical Applications of Negative Numbers http://mathforum.org/library/drmath/view/61468.html Negative Number History http://mathforum.org/library/drmath/view/52593.html I found these just by searching our site for "history zero" and "history negative". If you have any questions that are not answered there, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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