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In a course I took, the instructor gave a definition of hyperplane as follows:

Let $X$ be a vector space and $f:X\to\mathbb{R}$ a linear function. Then $M_a=\{x\in X|f(x)=a\}$ is called a hyperplane. $M_0=\{x\in X|f(x)=0\}$ is called a homogeneous hyperplane.

Then one of the homework the instructor gave us is to ask us to show that $M_0$ is a maximal proper subspace of $X$. But I think if $f=0$, then $M_0$ would be the whole $X$ which is not proper. So, should we add an additional requirement of $f\ne0$ in the definition of hyperplane? Thank you.

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Yes, you must exclude the zero-function. – Gerry Myerson May 4 '13 at 5:43
Thank you...... – Zhou Heng May 4 '13 at 5:47
up vote 1 down vote accepted

Community wiki answer so the question can be marked answered: Yes, you need to exclude the zero function.

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