Drawing Hasse Diagrams for Divisibility Relations

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Homework Statement


Draw the diagram P=(X,P) where X={1,2,3,5,6,10,15,30} and x<y in P IFF x divides y.


Homework Equations





The Attempt at a Solution


We just started this discussion in class and I am really not getting the concept of how to draw the corresponding Hasse diagram. I know that I am supposed to start with the smallest x for which x<y and for which there does not exist a z such that x<z<y. However, I don't know whether that should be a single element or an ordered pair when I list it on the diagram. I also know that I am only supposed to draw an edge if x is the preceding element to y. Anyway, that is pretty much all I understand about this concept. I appreciate any help in explanation of this concept.
 
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mblack said:

Homework Statement


Draw the diagram P=(X,P) where X={1,2,3,5,6,10,15,30} and x<y in P IFF x divides y.


Homework Equations





The Attempt at a Solution


We just started this discussion in class and I am really not getting the concept of how to draw the corresponding Hasse diagram. I know that I am supposed to start with the smallest x for which x<y and for which there does not exist a z such that x<z<y. However, I don't know whether that should be a single element or an ordered pair when I list it on the diagram. I also know that I am only supposed to draw an edge if x is the preceding element to y. Anyway, that is pretty much all I understand about this concept. I appreciate any help in explanation of this concept.

There's an article in wikipedia--http://en.wikipedia.org/wiki/Hasse_diagram. Maybe that will serve as a starting point for you.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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