Question

Let I denote the interval [0,oo). For each r (element of) I, define
Ar={(x,y)element of RxR:x^2+y^2=r^2}

Determine (UNION)reI Ar and (INTERSECT)reI Ar

Answer 1

The definition of Ar (Ar={(x,y)element of RxR:x^2+y^2=r^2}) means that for any r>0, Ar contains all points on the circle of radius r centered on the origin.

Answer 2

So how would you determine the Union & Intersection? I'm sure its simple...I'm just not getting it for some reason...as in how to write it out?

Answer 3

Consider that if ALL possible radii are included, than for every point (x,y) there will exist an Ar that contains it.

Also, can you say that every Ar contains different points, so that there does not exist a point (x,y) that exists in Ar for different r?