What does "wedge" mean? In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for $\wedge$, while $\vee$ is wirtten \vee. Where does this inconsistency come from?
A wedge refers to the shape of this object:



It doesn't matter if it's facing up or down, it's still a wedge. But since there was a need for two commands to produce $\wedge$ and $\vee$, and since $\vee$ conveniently looks like the letter V, it was probably decided that one should get the command "vee" and the other "wedge" (instead of something like "upwedge" and "downwedge", which would be harder to remember). But both are called "wedge" and it's up to the context to disambiguate.
The thing is that 'wedge' may also refer to the wedge product in the exterior algebra (or differential forms), which is also writen as $\wedge$.

I'm unaware of the real reason, you may try on TeX.SE, but coming from a geometrical background I believe this is how it should be, even though some topologists may disagree.