How to prove that the empty set is a half-open interval?

Question

Definition: $I$ is a half-open interval iff there exists $a \leq b \in \mathbb{R}$ s.t $I = \{ x \in \mathbb{R} : a \leq x < b \}$

My attempt:

Fix a particular $a,b \in \mathbb{R}$

Since the empty set has no elements at all, then there doesn't exist an $x \in \phi$ s.t $a >x>b$ then $\phi$ is a half-open interval by definition.

Is this correct?

Answer 1

Fix any $a\in\Bbb R$, then

$$\emptyset=\{x\in\Bbb R\mid a\le x<a\}$$