UNDERSTANDING NEGATIVE INTEGERS AS NATURAL NUMBER ORDERED PAIRS

• Main Author: yuliana, Resty
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46561
• Institution: Institut Teknologi Bandung

This project is aimed at understanding negative integers as natural number ordered pairs. So far, negative integers are understood using the number line or interpretation as debts that cause misconceptions especially among students. Negative integers have been known long before the 17th century. It can be seen in the text notes of the Babylonian in the second millennium BCE. Nevertheless, until the 19th century negative integers are still doubtful of its existence as a solution of algebraic equations, even Rene Descartes calls it the term ”false”. John Wallis (1616 ???? 1703) declared negative integers as opposed to positive numbers in the number line. Richard Dedekind (1831- 1916), defined negative integers as the inverse of a positive integers. Far earlier, Luca Pacioli (1494) stated negative integers as natural number ordered pairs. The concept of negative integers as natural number ordered pairs will be discussed in this project through the concept of the equivalence relation and equivalence class. The chosen approach is similar to the approach in understanding rational numbers and complex numbers as ordered pairs of known numbers.