Is this function both increasing and not injective?

Question

I'm supposed to come up with a function from $\mathbb R$ to $\mathbb R$ that is increasing and not injective. I came up with

$$f(x) = 1$$

which by my understanding is increasing and obviously not injective. Am I correct in believing this?

Answer 1

Yes $f(x)=1$ is increasing since $x_1>x_2\Rightarrow f(x_1) \geq f(x_2)$, but it is not strictly increasing, since $x_1>x_2 \nRightarrow f(x_1) > f(x_2)$.

Added: This seems to be an unfortunate clash with the 'common' (i.e. non-mathematical) usage of increasing, and in my experience this often causes surprise and misunderstandings.