Notation for a Point being between two Other Points

60 Views Asked by At

Let $x$, $y$ and $z$ be real numbers. Is there any notation that means that $x$ is between $y$ and $z$?

If $y$ is less than or equal to $z$, then the notation $y \leq x \leq z$ can be used, and there is similar notation when $z$ is less than or equal to $y$. I am asking for a notation that encompasses both of these possibilities.

2

There are 2 best solutions below

0
On BEST ANSWER

I am asking for a notation that encompasses both of these possibilities.

If you don't know whether $y \le z$ or $z \le y$, you could write: $$\min\left\{y,z\right\} \le x \le \max\left\{y,z\right\}$$

0
On

For real numbers $y,z$, the interval $[y,z]$ is given by $\{\lambda y + (1-\lambda)z\mid 0\leq \lambda\leq 1\}$.