One and Zero 3 The International Journal for the History of Mathematics Education The Numbers One and Zero in Northern European Textbooks

• Main Author: Kristín Bjarnadóttir
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Iceland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.475.7214; http://www.24grammata.com/wp-content/uploads/2011/11/Zero-24grammata.com_.pdf

One and zero have always existed in arithmetic textbooks. In the modern sense they are numbers. It has not always been so. The Greek view was that a number is a multitude of units. This was often interpreted to mean that one (1) was not to be understood as a number. The zero was introduced as a part of the Hindu-Arabic numeration, originally as a symbol to designate an empty slot. It was first presented as one of the ten digits in the early 13th century. For a long time it had a special position within the group of digits and was often called an insignificant digit. These views are reflected in Northern European writings that have influenced Icelandic arithmetic textbooks from the 13th century until the 19th. Examples from medieval times, as well as from the 17th, 18th and 19th centuries, are examined in this paper with respect to these views and in the light of contemporary cultural movements, such as the Enlightenment. During the last decades of the 19th century mathematicians and logicians made efforts to place the definition of a number on a sound basis. No evidence has been found that these matters were discussed in Iceland, while the ancient conceptions of one and zero disappeared from Icelandic textbooks in the early 20th century. Ideas on Zero and One and their Modernization In our modern number sense one and zero are counted as numbers, indeed very important numbers. Both belong to the set of integers. This is a recent representation. The ancient Greek mathematicians had a discrete view of number; that they were multiples of a unit, and Aristotle said that one is no number (Tropfke, 1980, p. 124). Euclid wrote in book 7, definitions 1 and 2: A unit is that by virtue of which each of the things that exist is called one.