I was reading Programming Languages and Lambda Calculi, which defines the multi-step reduction to be the reflexive-transitive closure of the one-step reduction. (Page 15, $\twoheadrightarrow_r$ is the reflexive-transitive closure of $\rightarrow_r$)
A quick search shows that this idea is widely accepted, for example by courses from Princeton, UPenn, CU, etc. However, I think the transtivity should be enough to capture the intuition of many steps. So why is reflexivity needed?