Soft question - are these two set notations correct?

Question

Do these sets equal the interval notation given? \begin{align} T&=\{t\in \mathbb{R}:t^2\lt{2}\}=(-\sqrt{2},\sqrt{2})\\ S&=\{s\in \mathbb{R}:s^2\leq{2}\}=[-\sqrt{2},\sqrt{2}] \end{align}

Answer 1

Yes, the sets do indeed equal the interval notation given.

You can sort of analogize why to when you solved inequalities in grade school:

$$x^2 < 2 \implies \left\{\begin{matrix} x < \sqrt 2 \\ x > - \sqrt 2 \end{matrix}\right. \implies -\sqrt 2 < x < \sqrt 2 \implies x \in (-\sqrt 2, \sqrt 2)$$

It was just always assumed back then (unless otherwise stated) $x$ was a real number. The setbuilder notation just explicitly states that (since you might not always deal with real numbers).