Transitive Relation/Examples/Less Than on Real Numbers

Example of Transitive Relation

Let $<$ be the usual ordering on the set of real numbers $\R$.

Then $<$ is a transitive relation, but neither reflexive nor symmetric.

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.5$ Relations: Example $1.3$
• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 7$: Relations