What does $f \lor g$ mean where $f,g$ are functions? I've encountered a problem asking me to prove that $f \lor g$ is lower-semi-comtinuous if $f,g$ are so. But I don't know what $f\lor g$ means... Any answer would be appreciated!
 A: This notation comes from lattice theory, where $\wedge$ means meet (i.e., greatest lower bound) and $\vee$ means join (i.e., least upper bound). In this context, $f \vee g$ is the function given by the pointwise maximum of $f$ and $g$, while $f \wedge g$ is their pointwise minimum.
(Personally, I don't know why some people prefer this notation over the clearer $\min(f,g)$ and $\max(f,g)$; the symbols look like they're pointing the wrong way to me. $f \vee g$ points down, but it means maximum.)
A: The notation you are searching for is: $ f \lor g = \dfrac{f+g+|f-g|}{2}$. Can you manage to define the $f \land g$ ?
A: As pointed out in the comments, this means the maximum $\max(f,g)$ between $f$ and $g$. The notation is common when dealing with posets, where $x\vee y$ is called the "join" of $x$ and $y$.
A: The notation $a \lor b$ means the maximum of $a$ and $b$. $a \land b$ means the minimum of $a$ and $b$.
This explanation is mnemonic; from a historical perspective it is not accurate.
There are many ways to remember this and explain the choice of symbol, but I like thinking of the minimum and maximum reading of $\land$ and $\lor$ as generalizations of their meaning in logic.
If we think of classical logic and use $0$ to mark false and $1$ to mark true, then $a \;\text{or}\; b$ the maximum of $a$ and $b$. This means we can think of the maximum in general as a generalization of $\lor$. The case for $\land$ is analogous.
