Hyperplanes

Given a space  
\[\mathbb{R}^n\]
, a hyperplane in  
\[\mathbb{R}^n\]
  is an  
\[n-1\]
  dimensional subspace.
A hyperplane is  
\[\mathbb{R}\]
  (of dimension 1) is a point (of dimension 0).
A hyperplane is  
\[\mathbb{R}^2\]
  (of dimension 2) is a line (of dimension 1).
Example:  
\[2x_1+3x_2=6\]

A hyperplane is  
\[\mathbb{R}^3\]
  (of dimension 3) is a plane (of dimension 2).
Example:  
\[2x_1+3x_2+4x_3=12\]

A hyperplane is  
\[\mathbb{R}^n\]
  (of dimension n) is a plane (of dimension n-1).
Example:  
\[2x_1+3x_2+...+4x_n=20\]

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