Conditional existence of real numbers Are there such numbers $a$ and $b$ that if $a < b$, then $a > b$ ?
Thanks.

I don't really think so. The condition $a < b$ implies that $a \ngeq b$ because $<$ is a total order on $\mathbb{R}$. If you're not familiar with orderings, they are just relations that are reflexive, anti-simmetric and transitive (see  Wikipedia. A set is said to be totally ordered if every element of the set can be compared to another with the ordering given. 
