Is [a, a[ empty?

Question

Is the segment $[a, a[$ equivalent to the point $\{a\}$ or the empty set $\varnothing$? Can one or other be formally proved?

I was wondering because in computer science it is the empty set, as the loop for(x = a; x < a; x+=incr) never executes.

Answer 1

It is defined as $\left[ a, b \right) := \left\{ x \in \mathbb{R} \vert a \leq x < b \right\}$ and with this it is the empty set because its elements have to satisfy $a \leq x < a$ and there is no such $x \in \mathbb{R}$ with this property.