Abstract
This chapter provides an overview of finite systems. A finite mathematical system can be produced by defining an operation of addition on a set of numbers S = {0, 1, 2, 3, 4, 5} arranged round a one-handed clock-face. Each separate addition starts with the hand at 0 and as each number is read so the hand is turned clockwise through that number of spaces until the sum is given by the final position of the hand. The chapter presents the definition of subtraction in terms of addition and subsequently describes subtraction as the inverse operation to addition. Just as subtraction can be defined in terms of addition, division can be defined in terms of multiplication. The multiplicative inverse of an element a is the element that multiplies a to give the multiplicative identity. The modal clock restricts the arithmetic to consider only the numbers that appear on its face. An arithmetic (mod m) can deal with the set of whole numbers but restricts all the results to a subset of the whole numbers by interpreting the results of a binary operation as a remainder after division by m.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
