When writing the solution to an inequality in interval notation, say $x < 5$ as $(-\infty, 5)$, how can the $x$ be "involved"?
Is it correct to just write $(-\infty, 5)$, or should it be $x=(-\infty, 5)$, or perhaps $x\in(-\infty, 5)$?
When writing the solution to an inequality in interval notation, say $x < 5$ as $(-\infty, 5)$, how can the $x$ be "involved"?
Is it correct to just write $(-\infty, 5)$, or should it be $x=(-\infty, 5)$, or perhaps $x\in(-\infty, 5)$?
One defines the interval $(-\infty, a)$ precisely as $\{x:x. So saying
$x\in (-\infty,a)$ is saying the same as saying
Note that writing $x=(-\infty, a)$ would only by correct if you're saying "All elements of $x$ are solution" (viz, $x$ would be denoting an set, not a real number). It is usual to write $S=(-\infty,a)$, where $S$ stand for "solution set", that is, all elements of $S$ are solutions.
The third option. You are in essence saying that $x$ belongs to the interval between $-\infty$ and $5$, or in other words, $x$ is contained in the set that includs all numbers larger than $-\infty$ and smaller than $5$.