Number of possible combinations of....

[Rosebud]

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?

 

[phinds]

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?

 

[Rosebud]

There are eight octants. I'm not sure about quadrants. EDIT: OK, I understand now. Thank you.

 

[phinds]

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?

 

[HallsofIvy]

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.

 

[phinds]

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.