Why the transitive closure for this relation $R = \{(x, y) \in \mathbb{R} \times \mathbb{R} \mid x < y\}$ is R?

Question

I have read a chapter on closures: reflexive, symmetric and transitive, and it seems I have not fully understand the concepts, at least for transitive closures.

Why the transitive closure for this relation $R = \{(x, y) \in \mathbb{R} \times \mathbb{R} \mid x < y\}$ is R?

Answer 1

because it'a transitive by itself