min/max

---

TODO: Flesh out this page - I created it only to document the $a\vee b:=\max(a,b)$ seen in Probability and Stochastics

---

Definition

Traditionally:

• $$\max(x,y):=\left\{\begin{array}{lr}x & \text{if }x\ge y\\ y & \text{otherwise}\end{array}\right.$$
• $$\min(x,y):=\left\{\begin{array}{lr}x & \text{if }x\le y\\ y & \text{otherwise}\end{array}\right.$$

Notations

$\min$	Definition	$\max$	Definition	Comment
$a\wedge b$	$a\wedge b:=\min(a,b)$	$a\vee b$	$a\vee b:=\max(a,b)$	I've not seen this notation used ANYWHERE else

See also

• Positive and negative parts of a function