[Math] Finding the infimum and supremum of an interval

Question

If I have $T = (1,2]$

I want to find infimum and supremum:

$\inf(T)$ is not possible / or negative infinity

$\sup(T) = 2$

Is this correct?

It is the $\inf(T)$ that I am confused about

Thank you.

Answer 1

$\inf(T)$ means the greatest lower-bound of $T$. We may state, for example, that all elements of $T$ are positive, so $0$ is a lower bound of $T$, which means that $\inf(T) \geq 0$. So your conclusion is clearly wrong.

In fact, we have $\inf(T) = 1$. Note that it is not necessary for $\inf(T)$ to be an element of $T$.