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Subspaces
The real three-dimensional space contains the following subspaces exactly:
| Dimension | Copies | Subspace |
|---|---|---|
| 0 | \(1 \times\) | the zero subspace, trivially |
| 1 | \(\infty\)-many | \(\mathbb{R}^1\) lines through the origin |
| 2 | \(\infty\)-many | \(\mathbb{R}^2\) planes through the origin |
| 3 | \(1 \times\) | \(\mathbb{R}^3\) itself, trivially |