What is the Definition of Zero? Who Invented the Symbol?
Date: 9 Jan 1995 12:18:50 -0500 From: David Chen Subject: Ask a question Hi, Dr. Math I am a student from Monta Vista's Internet class and I am here to ask you a question about math. I really wish that you can help me answer the questions. My question is: What is the definition of zero, and who invented or introduced the symbol to represent the zero? Thanks in advance. Sincerely, David Chen
Date: 10 Jan 1995 03:48:57 -0500 From: Dr. Sydney Subject: Re: Ask a question Dear David, Hello! I'm glad you wrote to Dr. Math. The concept of zero is surprisingly deep, and it took human thinkers quite a long time to come up with the notion of zero. In fact, though mathematicians began thinking about the concept of zero in 2000-1800 B.C.E., it was not until about 200-300 B.C.E. that the Babylonians began using a symbol that would evolve into what we today know as zero. It turns out that mathematicians first thought of zero in the context of writing numbers down -- zero was first a placeholder. Before mathematicians understood the notion of zero, there was much ambiguity about written numbers. For instance, if the symbol for 5 was written down, there was no way to tell what number was being expressed -- was it 5? Or, 50? Or, 5,000,000? Thus, zero was introduced as a placeholder to avoid these ambiguities. In India, the concepts of 0 as a placeholder and 0 as a number were associated with one another much earlier than in Babylon. It is from the Indians that we get our present-day symbol for 0. I don't have an exact definition for 0 here with me at home. I can tell you this: when working with sets or groups of elements under some defined operation of addition, the "zero element" is defined as the element, let's call it z, such that a + z = a for all a in the set or group. So, one definition you could use for 0 is that 0 + x = x for all real numbers x. Alternatively, you might define 0 as the number in between the positive and negative numbers. Or, maybe you could define 0 as lacking quantity (that's what the dictionary says!) What do you think about these different definitions? If you are looking for a different definition, write us back, and we'll try to find a better one. I hope this helps. Write back if you have any questions. --Sydney, Dr. "whoa" math
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.