- #1
gravenewworld
- 1,132
- 26
Show that the set of points on a line is equinumerous with the set of points in space.
If you consider R^3, then sum(x,y,z) for all ordered triples will get mapped to some real number. But what function can I make so that I can take all real numbers so that they will map to some ordered triple? All I need is 1 bijective function or two total functions ( 1 going from R^3-->R and 1 going from R--->R^3) to show that the two sets are equinumerous right?
If you consider R^3, then sum(x,y,z) for all ordered triples will get mapped to some real number. But what function can I make so that I can take all real numbers so that they will map to some ordered triple? All I need is 1 bijective function or two total functions ( 1 going from R^3-->R and 1 going from R--->R^3) to show that the two sets are equinumerous right?