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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/360729
Title: 
A path through the lattice points in a quadrant
Author(s): 
Beck, George
Language: 
eng
Description: 
  • Integers
  • Let Z+={1,2,3,...} be the set of positive integers. The set of lattice points in the first quadrant is the set Z+*Z+={(1,1);(1,2),...}, where both coordinates are positive integers. Even though is two-dimensional, it is possible to set up a one-to-one correspondence between Z+*Z+ and ℤ+, as shown in the picture. By associating (m/n) with the lattice point (m,n) the path through the lattice points gives an enumeration of the positive unreduced rational numbers. Skipping past the fractions that have a common factor gives a listing of the positive rational numbers. The matching shows that there are as many positive fractions as positive integers. In spite of that, there are differences between the integers and the rationals; for example, between any two rationals there is another rational
  • Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática
Issue Date: 
  • 11-Sep-2008
  • 11-Sep-2008
  • 2008
  • 11-Sep-2008
  • 9-Sep-2008
Keywords: 
  • Analysis
  • Foundations of Mathematics
  • Educação Superior::Ciências Exatas e da Terra::Matemática::Análise Numérica
Notes: 
Show a path through the Lattice Points in a Quadrant
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/5217
URI: 
http://acervodigital.unesp.br/handle/unesp/360729
Rights: 
Demonstration freeware using Mathematica Player
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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