ℝ^3 space

HelpNeeder

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Feb 17, 2021
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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

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Mar 3, 2021
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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
 

Jomo

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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

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

HelpNeeder

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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

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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

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Alright, thank you!
 
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