Number of possible combinations of....

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To find all combinations of the point (x,y,z) where each variable can be either positive or negative, one must consider the eight possible octants in three-dimensional space. Each variable can independently take on two values (positive or negative), leading to a total of 2^3 combinations, which equals eight distinct points. The discussion clarifies the terminology, noting that while two dimensions have four quadrants, three dimensions are divided into eight octants. Understanding this concept helps in determining the signs of each variable for every combination. The exploration of these combinations highlights the relationship between dimensions and the number of possible sign configurations.
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How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct point?
 
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Rosebud said:
How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct point?
In 3D coordinates, how many "quadrants" are there?
 
There are eight octants. I'm not sure about quadrants. EDIT: OK, I understand now. Thank you.
 
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Rosebud said:
There are eight octants. I'm not sure about quadrants.
Right. So how many ways could you have the point positioned, from the point of view of differing signs?
 
As the names imply, in two dimensions there are four "quadrants" and in three dimensions there are eight "octants. In n dimensions there are 2^n such subsets.
 
Rosebud said:
There are eight octants. I'm not sure about quadrants.
Yeah, that's why I put "quadrants" in quotes, to mean just "sections", which you more appropriately identified as octants.
 

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