Is it possible to make graphs of subsets of Rational Numbers in Mathem

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SUMMARY

Graphing subsets of rational numbers in Mathematica is not feasible due to the density of rational numbers in any interval, such as [0, 1]. Users cannot create a graph that accurately represents rational numbers without including irrational numbers. A workaround involves using a tablet and OneNote to manually illustrate the concept with open circles, but this does not provide a precise mathematical representation.

PREREQUISITES
  • Understanding of rational numbers and their properties
  • Familiarity with Mathematica plotting commands
  • Basic knowledge of mathematical graphing concepts
  • Experience with digital drawing tools like OneNote
NEXT STEPS
  • Explore Mathematica's plotting functions for visualizing mathematical sets
  • Research the concept of density in rational numbers
  • Learn about alternative methods for representing mathematical concepts visually
  • Investigate other digital tools for mathematical illustration
USEFUL FOR

Mathematicians, educators, students, and anyone interested in visualizing mathematical concepts, particularly those involving rational numbers and graphing techniques.

MidgetDwarf
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Is it possible to make subsets of rational numbers in Mathematica using the plot command, or any other command? Ie., say I want to graph the set of rational numbers from 0 to 1.
 
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The rationals are dense in [0,1]. What do you mean by "make subsets"? How would you "graph" a set?
 
Thats what I was thinking. Due to the density of ℚ its not possible. By graphing, I meant if it was possible to create a segment of say length 1, with "holes" (no irrationals). Ofcourse, it would not be an exact, but something that approximated it.

Anyways, it cannot be done. I found a workaround by using a tablet and using one note to draw open circles to illustrate what I was aiming for.

Thanks.
 

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