Wikipedia:Reference desk/Archives/Mathematics/2016 November 8

= November 8 =

If the Greeks did not have the "0" zero
Then, if they had subtraction, and I assume they did, what would be the output of 1-1? Or was it the case that the Greeks did not have "0" zero in their notation, but obviously understood the concept of "nothing left"? --Hofhof (talk) 01:08, 8 November 2016 (UTC)


 * Might be better to call it a Zero.--Aspro (talk) 01:27, 8 November 2016 (UTC)


 * Whatever. --Hofhof (talk) 02:28, 8 November 2016 (UTC)


 * "Not having the concept of zero" just means not to consider it to be a proper number. Consider these two answers to the Q: "How much money do I owe you ?"


 * A) "You owe me zero dollars and cents."


 * B) "Your assumption that you owe me money is incorrect. You don't owe me anything."


 * Answer B is what you might expect from a culture without zero as a mathematical concept. Note that the same info is conveyed in each case.  As far as writing down zero as an amount, they might right "N/A", a dash, or any number of things to show that there is no number.  StuRat (talk) 03:38, 8 November 2016 (UTC)
 * It is interesting to see in this context the description from disjoint sets as described in article to have no elements in common, phrasing similar to B) statement.--82.79.115.216 (talk) 02:46, 13 November 2016 (UTC)
 * The Egyptians used the symbol for beautiful when numbers balanced in accounts and for a base point in building - and they had negative amounts from that too. But yes I agree saying zero cows would probably be almost as silly for them as talking about negative cows. Dmcq (talk) 10:08, 8 November 2016 (UTC)


 * I see this discussion and I've just spotted the historical info from 0_(number) about Egiptian accounting texts and also Pre-Columbian Americas.--5.2.200.163 (talk) 16:02, 10 November 2016 (UTC)


 * Sounds like a datum point. Note that saying "zero cows" sounds a bit silly to us too, as we still tend to think of zero not as a number, but as the lack of a number. StuRat (talk) 21:25, 8 November 2016 (UTC)


 * For many people it doesn't seem particularly troubling for an arithmetic operation to not produce an answer. Mathematically unsophisticated people today might say that 3 - 5 has no answer, since negative numbers are not in their repertoire.  Similarly, sqrt(2) has no answer unless you accept irrational numbers and sqrt(-1) has no answer unless you accept complex numbers.  Also, classical Greek mathematicians not only did not accept zero as a number, they did not accept ONE as a number.  By their definition, a number measures a plurality of units, and one was a unit, not a plurality.  So proofs in Greek mathematics often seem very cumbersome today, since they had to treat separately the cases that handled "one" vs. cases that handled "more than one".  CodeTalker (talk) 22:22, 8 November 2016 (UTC)


 * It seems that some philosophical infiltrations in the form of ontological paradoxes have interfered with the development of some mathematical concepts.--5.2.200.163 (talk) 16:06, 10 November 2016 (UTC)


 * An interesting Q is how computers might handle zero if we had t no symbol for it. They could always print out something like NaN, which they sometimes print out for a division by zero error, etc. StuRat (talk) 18:05, 9 November 2016 (UTC)


 * Surely there is a typo in your wording to symbol instead of no symbol.--5.2.200.163 (talk) 16:12, 10 November 2016 (UTC)


 * Corrected. Thanks. StuRat (talk) 19:57, 12 November 2016 (UTC)


 * I have two comments. First, more importantly, we should remember that a zero is a counter-intuitive concept unless we have learned it as an inherent part of mathematics in elementary school.  It is counter-intuitive because it is a symbol that doesn't represent anything, because it represents nothing.  I am aware that I will get replies that that statement oversimplifies, but any statement to that effect is a statement from the standpoint of someone with a modern mathematical education.  Second, although the ancient Greeks in general didn't have a symbol for zero, ancient Greek astronomers and astrologers did use the equivalent of a zero when they were doing calculations using Babylonian mathematics using base sixty.  Robert McClenon (talk) 16:53, 10 November 2016 (UTC)


 * I have some remarks: Interesting and surprising situation you mention about the use of the equivalent of a zero in calculations by ancient Greek astronomers, although they didn't have a symbol for zero. About the counter-intuitive nature of the concept zero it is interesting to see the contexts in which the counter-intuitiveness makes its way into mathematical reasoning as a necessity, for instance in the difference of two equal numbers.--5.2.200.163 (talk) 12:08, 11 November 2016 (UTC)


 * Thinking about an abacus might make it more obvious. On an abacus what we consider as a zero can also be considered as an absence. One does not need to add an absence. One does not need to multiply by an absence. And a position on an abacus with an absence of anything still exists as a a position as in Babylonian numbers. When one subtracts two equal numbers one might find there is no difference between them, or as the Egyptians put it their accounts were beautiful. Or in relation to their building plans a point might be before or after a base point by a certain amount - or might be the actual base point. In all that one doesn't need to have zero as a number that can be added or multiplied or as a a distance from a place. Dmcq (talk) 13:57, 11 November 2016 (UTC)


 * Not having zero would make the notion of a group harder to describe. It also would make negative numbers harder to describe.--Jasper Deng (talk) 19:52, 12 November 2016 (UTC)


 * Could also the concept of infinitesimal or limit be harder to describe without an explicit notion of zero?--82.79.115.216 (talk) 02:50, 13 November 2016 (UTC)


 * I wouldn't think so. Just as you could say "the limit is x, as y approaches the number 0", you could also say "the limit is x, as y approaches the non-number nil". StuRat (talk) 15:30, 13 November 2016 (UTC)