What is the union symbol (#uu#) used for?

In Pre-Calculus, union is used in #(x_1,x_2) uu (x_3,x_4)#, which basically means "join together the lefthand and righthand domains". Similarly, in a geometry class, it means "join together the lefthand and righthand shapes".

So something like:

#(-oo,0) uu (0,oo) in ZZ#

in Pre-Calculus could be read as "the set of integers in which the domain extends from negative infinity to 0 and 0 to infinity, except for 0".

It says that you have a "joint" domain where all integers #ZZ# (let's assume they are real) are available, except for #0#. So, you have the following set of numbers:

#-oo, ... -2, -1, 1, 2, ..., oo#

Or, if you have this in a geometry class:

#DeltaABC uu DeltaBCD#

if #bar(BC)# is the shared side that vertically bisects a bigger general (non-right) triangle #DeltaACD#, it could join an ABC right triangle with a BCD right triangle, like pushing together puzzle pieces.

Consider the example below. The concept of geometric unions is used (incompletely here) to demonstrate why the area of a triangle is #1/(wh)#

The following geometric union statements are applicable:

#color(white)("XXXX")##squareACDF =triangleAB_1Fuutriangle FBDuutriangleDB_2C#

#color(white)"XXXX"##triangle BFD = triangle FB_1B_2 = triangle FB_1AuutriangleDB_2C#