Show that the number of multiples of $m$ in $[1, x]$ is $\lfloor \frac{x}{m} \rfloor$

I'm self-studying number theory using "A Computational Introduction to Number Theory and Algebra" by Victor Shoup, and this trivially-looking exercise throws me off:

Let $m$ $\in$ $\mathbb{Z}$, $m$ $\gt$ 0; $x$ $\in$ $\mathbb{R}$, $x$ $\ge$ 1. Show that the number of multiples of $m$ in $[1, x]$ is $\lfloor \frac{x}{m} \rfloor$

Let's take $x = 4.0$ and $m = 2$. Then $\lfloor \frac{x}{m} \rfloor = 2$. But I don't see two multiples of $m$ in $[1, 4.0]$:

• first multiple goes from 1 to 3
• second multiple goes from 3 to 5, and 5 $\notin [1, 4.0]$

What am I missing? This feels so elementary I'm even ashamed of asking