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

Gold Member
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.

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phinds

Gold Member
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

Homework Helper
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

Gold Member
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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