What do two 'greater than' symbols mean
I'm working through the basic math course on brilliant.org and I found an answer I don't understand here. (The 2nd part of the 4th answer option).
What does this mean?
-10 < a < 0Is there an implicit AND after a ? And therefore does it mean this?
-10 < a AND -10 < 03 Answers
$\begingroup$There is an implied AND, but not in the way you put it. It really means
$$-10 < a\quad\text{AND} \quad a<0 $$
In other words, $a$ is between $-10$ and $0$, excluding end points. In general, $x_1 < x_2 < x_3 <... < x_n$ means $$x_1 < x_2\quad\text{AND} \quad x_2 < x_3 \quad\text{AND} \quad x_3 < x_4 \quad ...\quad x_{n-2} < x_{n-1} \quad\text{AND} \quad x_{n-1} <x_n $$
$\endgroup$ 4 $\begingroup$it means that $a$ is between $-10$ and $0$
so $a<0$ and $a>-10$
$\endgroup$ $\begingroup$There is an implicit AND but not the way you think.
$-10 < a < 0$ means $-10 < a$ AND $a < 0.$
It is a convenient way to express the values a can take given an upper and a lower limit.
$\{x \mid -10 < a < 0\}$ is equivalent to $(-10, 0)$ in interval notation.
$\endgroup$ 1
