I'm having difficulty understanding irreflexive relations.
I have the definition of an irreflexive relation as: a relation $R$ over a set $A$ if for any $x \in A$, $xRx$ doesn't hold.
Many sources indicate that the relation "less than", for example, is irreflexive in this way ($x<x$ doesn't hold).
My question is: why not? Isn't $x<x$ simply "false"? I may be misunderstanding the meaning of "$xRx$ holds (or doesn't hold)".
For context, my background is in software development, which may be clouding my intuition. It's not as though the expression $2<2$ wouldn't compile, for example; it would just return false, but it seems this isn't mathematically accurate.