# ℝ^3 space

#### HelpNeeder

##### New member
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

##### Junior Member
When we say that a few vectors span $$\displaystyle ℝ^3$$, what is actually meant by $$\displaystyle ℝ^3$$? The whole three-dimensional space?
Yes

• HelpNeeder

#### Jomo

##### Elite Member
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.

• HelpNeeder

#### HallsofIvy

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

• HelpNeeder

#### HelpNeeder

##### New member
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

##### Elite Member
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

##### New member
Alright, thank you!