Domain of z= ln ( (x^2) + (y^2) )

[chetzread]

Homework Statement

the given ans is x ≠ 0 , y ≠ 0 , the ans given is x ≠ 0 , y ≠ 0 . I don't understand the ans , why the author leave the ans like this ?

IMO , x can be 0 as long as y not = 0
y also can be 0 , as long as x not = 0 ,by giving the ans in x ≠ 0 , y ≠ 0 , the author just rule out the possibility above ?

Homework Equations

The Attempt at a Solution

 

[mfb]

I guess "x ≠ 0 , y ≠ 0" was meant as "x ≠ 0 or y ≠ 0". The comma is misleading here.

 

[Mark44]

I guess "x ≠ 0 , y ≠ 0" was meant as "x ≠ 0 or y ≠ 0". The comma is misleading here.

I agree. A comma is typically used as shorthand for "and".