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

In summary, the conversation discussed the possibility of creating subsets of rational numbers using Mathematica's plot command. It was determined that due to the density of rational numbers in the given range, it is not possible to accurately graph a segment with "holes" representing irrationals. However, a workaround was found using a tablet and drawing open circles on OneNote to illustrate the desired concept.
  • #1
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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  • #2
The rationals are dense in [0,1]. What do you mean by "make subsets"? How would you "graph" a set?
 
  • #3
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.
 

1. Can graphs be used to represent subsets of Rational Numbers in Math?

Yes, graphs can be used to represent subsets of Rational Numbers in Math. Graphs are visual representations of data, and subsets of Rational Numbers can be represented using points or lines on a graph.

2. How are subsets of Rational Numbers graphed?

Subsets of Rational Numbers can be graphed by plotting the numbers on a number line or by using coordinates on a coordinate plane. The points on the graph correspond to the Rational Numbers in the subset.

3. What are the advantages of using graphs to represent subsets of Rational Numbers?

Graphs can provide a visual representation of the relationship between numbers in a subset of Rational Numbers. They can also make it easier to identify patterns, compare values, and make predictions.

4. Are there any limitations to using graphs for subsets of Rational Numbers?

One limitation of using graphs for subsets of Rational Numbers is that they can only represent a finite number of numbers. Also, not all subsets of Rational Numbers can be accurately represented on a graph.

5. Can graphs be used to perform operations on subsets of Rational Numbers?

Yes, graphs can be used to perform operations on subsets of Rational Numbers. For example, addition and subtraction can be represented by moving points along the number line, and multiplication and division can be represented by changing the scale of the graph.

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