The multiplication of negative numbers

Algebra ◽  
2004 ◽  
pp. 18-21
Author(s):  
Israel M. Gelfand ◽  
Alexander Shen
Keyword(s):  
Negative Numbers

Exploring the Boundaries of the Number–Temporal Order Association

2015 ◽  
Vol 62 (3) ◽  
pp. 198-205 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Embodied Cognition ◽  
Mental Representation ◽  
Temporal Order ◽  
Past Research ◽  
Numerical Comparison ◽  
Negative Number ◽  
Comparison Task ◽  
Negative Numbers ◽  
The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

Positive Psychology’s A Priori Problem

2017 ◽  
Vol 58 (3) ◽  
pp. 313-342 ◽  
Author(s):  
Barbara S. Held
Keyword(s):  
Conceptual Framework ◽  
A Priori ◽  
A Posteriori ◽  
Negative Numbers ◽  
Psychological States ◽  
Psychological Reality ◽  
Negative Results ◽  
Optimal Functioning ◽  
Conceptual Muddles ◽  
Negative Phenomena

The positive/negative distinction works well in many fields—for example, in mathematics negative numbers hold their own, and in medical pathology negative results are usually celebrated. But in positive psychology negativity should be replaced with positivity for flourishing/optimal functioning to occur. That the designation of the psychological states and processes deemed positive (good/desirable) and negative (bad/undesirable) is made a priori, independent of circumstantial particularity, both intrapersonal and interpersonal, does not seem to bother positive psychologists. But it should, as it results in conceptual muddles and dead ends that cannot be solved within their conceptual framework of positivity and negativity. Especially problematic is an ambiguity I find in positive psychologists’ a priori and a posteriori understandings of positivity and negativity, an ambiguity about constitutive and causal relations that pervades their science and the conclusions drawn from it. By eliminating their a priori dichotomy of positivity and negativity, positive psychologists might well find themselves in a better position to put back together the psychological reality that they have fractured in their ontologically dubious move of carving up psychological reality a priori into positive and negative phenomena. They then might find themselves better placed to “broaden and build” their own science of flourishing.

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

On a Discrete Analogue of Inequalities of Opial and Yang

1968 ◽  
Vol 11 (1) ◽  
pp. 73-77 ◽  
Author(s):  
Cheng-Ming Lee
Keyword(s):  
Integral Inequality ◽  
Discrete Analogue ◽  
Absolutely Continuous ◽  
Negative Numbers ◽  
Image Position

Let be a non-decreasing sequence of non-negative numbers, and let U∘=0. Then we haveYang [3] proved the following integral inequality:If y(x) is absolutely continuous on a≤x≤X, with y(a) = 0, then

scholarly journals DEPLESI SUMBER DAYA IKAN TUNA DAN CAKALANG DI INDONESIA

2019 ◽  
Vol 13 (2) ◽  
pp. 167
Author(s):  
Maulana Firdaus ◽  
Akhmad Fauzi ◽  
A Faroby Falatehan
Keyword(s):  
Resource Depletion ◽  
Production Model ◽  
Economic Potential ◽  
Average Volume ◽  
Negative Numbers ◽  
Average Value ◽  
Surplus Production ◽  
Fish Resources ◽  
Surplus Production Model ◽  
The World

ABSTRAKTuna dan cakalang memiliki potensi ekonomi yang besar di Indonesia. Beberapa penelitian menunjukkan bahwa kedua komoditas ini telah menunjukkan gejala over fishing di dunia, termasuk Indonesia. Penelitian ini bertujuan untuk mengestimasi seberapa besar deplesi ikan tuna dan cakalang di Indonesia. Deplesi sumber daya dihitung melalui perkiraan stok dan tingkat hasil lestari dengan menggunakan model produksi surplus dan estimasi parameter menggunakan metoda Clarke Yoshimoto Pooley (CYP). Nilai deplesi diperoleh dari perkalian volume deplesi dengan unit rent. Hasil penelitian menunjukkan bahwa volume rata-rata deplesi sumber daya ikan tuna dan cakalang pada periode 1992-2015 adalah (-) 2.828 ton per tahun. Rata-rata nilai deplesi sumber daya ikan tuna dan cakalang menunjukkan angka negatif, yaitu (-) Rp131,89 miliar per tahun. Nilai negatif ini menunjukkan bahwa selama periode 1992-2015, stok sumber daya ikan tuna dan cakalang mengalami penurunan sebesar 2.828 ton per tahun dengan nilai potensi kerugian atau kehilangan akibat penurunan stok yang mencapai Rp131,89 miliar per tahun.Title: Tuna And Skipjack Resources Depletion In IndonesiaABSTRACTTuna and Skipjack has a great economic potential in Indonesia. Several studies have shown that these commodities have symptomed of over-fishing in the world, including Indonesia. This study aims to estimate the extent of tuna and skipjack depletion in Indonesia. Resource depletion is calculated through stock estimates and sustainable yield levels using surplus production model and parameter estimation of Clark Yoshimoto Pooley (CYP) method. Depletion value is obtained from multiplication of depletion volume with unit rent. Results of the study showed that the average volume of depletion of tuna and skipjack resources in the period 1992-2015 was (-) 2,828 tons per year. The average value of tuna and skipjack resource depletion showed negative numbers, ie (-) IDR 131.89 billion per year. This negative value indicates that during the period 1992-2015, the stock of tuna and skipjack fish resources decreased by 2.828 tons per year with the potential value of loss or loss due to a decrease in stock which reached IDR131,89 billion per year. 

scholarly journals Analysis of relative abundances on environmental gradients

2018 ◽  
Author(s):  
Fiona Chong ◽  
Matthew Spencer
Keyword(s):  
Compositional Data ◽  
Environmental Gradients ◽  
Compositional Data Analysis ◽  
Depth Gradient ◽  
Negative Numbers ◽  
Marine Communities ◽  
Rates Of Change ◽  
Compositional Approach ◽  
Vertical Slice ◽  
Relative Abundances

Ecologists often analyze relative abundances, which are compositions (sets of non-negative numbers with a fixed sum). However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.

The New Entities of Abbacus and Renaissance Algebra

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Fifteenth Century ◽  
Middle Ages ◽  
Natural Science ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Northern Italy ◽  
Historical Narrative ◽  
Negative Numbers ◽  
Late Middle Ages ◽  
Mathematical Signs

This chapter offers a historical narrative of some elements of the new algebra that was developed in the fourteenth to sixteenth centuries in northern Italy in order to show how competing philosophical approaches find an intertwining expression in mathematical practice. It examines some of the important mathematical developments of the period in terms of a “Yes, please!” philosophy of mathematics. It describes economical-mathematical practice with algebraic signs and subtracted numbers in the abbaco tradition of the Italian late Middle Ages and Renaissance. The chapter first considers where the practice of using letters and ligatures to represent unknown quantities come from by analyzing Benedetto's fifteenth-century manuscript before discussing mathematics as abstraction from natural science observations that emerges from the realm of economy. It also explores the arithmetic of debited values, the formation of negative numbers, and the principle of fluidity of mathematical signs.

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