Examples of semi-norms on the real line

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?

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

For example, we have the function $\lvert \lvert x \rvert \rvert=0$.