Rafael Núñez Department of Cognitive Science University of California, San Diego La Jolla, CA, USA [email protected] Abstract What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early c...

Floating-point numbers are an essential part of modern software, recently gaining particular prominence on the web as the exclusive numeric format of Javascript. To use floating-point numbers, we require a way to convert binary machine representations into human readable decimal outputs. Existing conversion algorithms make trade-offs between completeness and performance. The classic Dragon4 alg...

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of sy...

Since a statement of number based on counting contains an assertion about a concept, in a logically perfect language a sentence used to make such a statement must contain two parts, first a sign for the concept about which the statement is made, and secondly a sign for a second-order concept. These second-order concepts form a series and there is a rule in accordance with which, if one of these...

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Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation. Participants (N = 44) completed two tasks. In the Eval...

A finite arithmetic sequence of real numbers has exactly two generators: the sets {a, a+f, a+2f, . . . a+ (n − 1)f = b} and {b, b − f, b − 2f, . . . b − (n − 1)f = a} are identical. A different situation exists when dealing with arithmetic sequences modulo some integer c. The question arises in music theory, where it has long been acknowledged that certain musical scales are generated, i.e. are...

Initial numeration is part of the math skills that every student must have. However, children with autistic disorder do not have good initial numeracy skills. This study aims to analyze abilities students disorders. research case research. The subjects this were 2 class III, namely boys and girls. Data collection techniques used in interviews, observation, test sheets related analysis are carri...

The relative linguistic transparency of the Asian counting system has been used to explain Asian students' relative superiority in cross-cultural comparisons of mathematics achievement. To test the validity and extent of linguistic transparency in accounting for mathematical abilities, this study tested Chinese and British primary school children. Children in Hong Kong can learn mathematics usi...

Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have imp...