ℝ^3 space

[HelpNeeder]

When we say that a few vectors span ℝ³, what is actually meant by ℝ³? The whole three-dimensional space?
Can we show it on a graph?

 

[lex]

When we say that a few vectors span [MATH]ℝ^3[/MATH], what is actually meant by [MATH]ℝ^3[/MATH]? The whole three-dimensional space?

Yes

 

[Steven G]

R³ = set of all vectors in the form (a, b, c) where a, b and c are real numbers.
If you mean graph R³ on a sheet of paper, then I wonder if that is true. How can you graph a the point in space on a 2-D piece of paper? This is just my option.

 

[HallsofIvy]

The OP did not say the graph had to be on a sheet of paper. You can graph R^3 in three dimensions.

 

[HelpNeeder]

The OP did not say the graph had to be on a sheet of paper. You can graph R^3 in three dimensions.

And that graph will be infinite?

 

[HallsofIvy]

Yes, \(\displaystyle R^3\) is the mathematical model for all of space so is infinite.
You may not be able to represent all of \(\displaystyle R^3\) whether on paper or some three dimensional format.

 

[HelpNeeder]

Alright, thank you!