The interval $(-√2, √2)$ represents the set of all real numbers $x$ such that:

$-√2 < x < √2$

Explanation:

1. Open Interval: The parentheses $($) indicate that the endpoints $-√2$ and $√2$ are not included in the interval.
2. Graphical Representation: On a number line, this interval includes all numbers strictly between $-√2$ and $√2$ but excludes the endpoints themselves.

Example Values in the Interval:

• $x = 0$
• $x = 1$
• $x = -1.5$
• $x = 1.414$ (approximately $\sqrt{2}$ but strictly less than it)

Set Notation:

$\{x \in \mathbb{R} : -√2 < x < √2\}$

Use Cases:

Such intervals are often used in calculus, real analysis, or problems involving constraints on real numbers.

Would you like more details or have further questions? Here are five related questions:

1. What is the difference between open, closed, and half-open intervals?
2. How do you represent intervals graphically on a number line?
3. Can you evaluate the length of this interval?
4. What are some functions defined only on this interval?
5. How would this interval change if it were $[-√2, √2]$?

Tip: Always check whether endpoints are included or excluded when interpreting intervals.