TITLE: Is $[a, a)$ equal to $\{a\}$ or $\varnothing$?
QUESTION [6 upvotes]: Let us define the set $[a,b) = \{ x \in \mathbb{R}: a\le x <b\}$
Is $[a, a)$ equal to $\{a\}$ or $\varnothing$?

REPLY [11 votes]: You can write the conditions as follows: $[a,a)=\left\{x\in\mathbb{R}: a\leq x<a\right\}$. Now, since there is no real number fulfilling this condition (which, if fulfilled, implies $a<a$), the set must be empty.

REPLY [2 votes]: You can think of $[a,b) = (-\infty,b) \cap [a,\infty)$. Choose $b=a$ :D