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I just would like to solicit some examples of semi-norms on the set $\mathbb{R}$? Of course, one such examples is the absolute value function. Are there any examples?

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  • $\begingroup$ This is immediate from the definition. $\endgroup$ – David C. Ullrich Jul 22 '15 at 20:24
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    $\begingroup$ Sir David, what i want is an example of a semi-norm on $\mathbb{R}$ other than the absolute value function. $\endgroup$ – Juniven Jul 22 '15 at 20:27
  • $\begingroup$ What makes you think I didn't understand what you want? $\endgroup$ – David C. Ullrich Jul 22 '15 at 20:28
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    $\begingroup$ an explicit example of a semi-norm other than the absolute value function? $\endgroup$ – Juniven Jul 22 '15 at 20:31
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    $\begingroup$ The family of seminorms on $\mathbb{R}$ is rather boring. $\{ x \mapsto c\cdot \lvert x\rvert : c \in [0,+\infty)\}$ $\endgroup$ – Daniel Fischer Jul 22 '15 at 21:10
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For example, we have the function $\lvert \lvert x \rvert \rvert=0$.

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