Arithmetic computation with probability words and numbers

Arithmetic With Complex Numbers

Write words with numbers

Write each as a numeral. 1) six hundred twenty-four thousand, five hundred four 2) six hundred ninety-nine thousand, ninety-eight 3) four hundred thousand, five hundred thirty-seven 4) three hundred thirty thousand, four hundred eighteen 5) three thousand, one hundred ninety-six 6) two thousand, eight hundred 7) five thousand, one hundred ninety 8) eight thousand, fourteen 9) ninety thousand, n...

Computation with the Extended Rational Numbers and an Application to Interval Arithmetic

Programming languages such as Common Lisp and virtu ally every computer algebra system CAS support exact arbitrary precision integer arithmetic as well as exact ra tional number computation Several CAS include interval arithmetic directly but not in the extended form indicated here We explain why changes to the usual rational number system to include in nity and not a number may be use ful espe...

Fuzzy Arithmetic with Parametric LR Fuzzy Numbers

Lyndon words and Fibonacci numbers

It is a fundamental property of non-letter Lyndon words that they can be expressed as a concatenation of two shorter Lyndon words. This leads to a naive lower bound ⌈log 2 (n)⌉ + 1 for the number of distinct Lyndon factors that a Lyndon word of length n must have, but this bound is not optimal. In this paper we show that a much more accurate lower bound is ⌈logφ(n)⌉ + 1, where φ denotes the gol...