# Any shortcut to remember least upper bound $\vee$ and greatest lower bound $\wedge$ in Lattice concept

I know this is silly but I am every time forgetting lub (least upper bound) in lattice as $$\vee$$ and glb (greatest lower bound) as $$\wedge$$. Is there any shortcut or mnemonic for remembering which one is join and which one is meet? Is there any historical reason for choosing such symbols?

• With respect to inclusion, the lub of two sets is $A\cup B$ and the glb is $A\cap B$. Commented Oct 6, 2020 at 20:10
• this is nice sir. thank you Commented Oct 6, 2020 at 20:30

If you think about logical operations as binary operations on $$\{0,1\}$$ under the identification $$\text{True}=1$$ and $$\text{False}=0$$, then $$\land$$ coincides with $$\min$$ and $$\lor$$ coincides with $$\max$$.
I too have struggled with this notation when I first learned about lattice theory. I am glad to see that I am not alone in this confusion. Something making the notation particularly confusing is there is a "v" shape in the Hasse diagram of a lattice formed by $$x \wedge y$$, $$x$$ and $$y$$ (if $$x$$ and $$y$$ are incomparable yadda yadda...) and a wedge shape in the Hasse diagram of a lattice formed by $$x \vee y$$, $$x$$ and $$y$$. But something I have not thought about until now is that if we draw Hasse diagrams upside-down, this is no longer an issue.
Like Angina mentioned, $$\cup$$ and $$\cap$$ mimic the shape of $$\vee$$ and $$\wedge$$. My hypothesis is that, since Boolean algebras were studied before general lattices, that $$\cup$$ and $$\cap$$ were the only notation. Then, somewhere along the way, the symbols were drawn a bit differently to distinguish between sets and elements of an abstract lattice.
In my opinion, the symbol $$\wedge$$ is used way to frequently in mathematics. E.g. the smash product in topology, exterior algebra of a vector space (in particular, differential forms), lattice meet, logical AND etc. (there are probably more, maybe a use in analysis?). Unfortunately, while you and I may not like the meet/join notation, we are stuck with it as the notation has stood the test of time.