Is $a\in[a,a)$?

Question

The title is my question, no more things.

Answer 1

$[a,b)$ is defined as $\{x:\ a\leq x < b\}$. If $a=b$ then the inequality $a\leq x < a$ is never satisfied. Therefore the set is empty.

Answer 2

No, as $[a,a)$ means $a \le a $ and $a<a$ according to Baby Rudin. The second inequality is clearly false, so the set $[a,a)=\varnothing$.