Abstract Algebra 75: In a field F, why does xy=0 imply either x=0 or y=0?

Abstract Algebra 75: In a field F, why does xy=0 imply either x=0 or y=0?

Abstract: Let F be a field, and let x and y be two elements in F that satisfy xy=0. We prove this implies that either x=0 or y=0 or both!

This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:

[faditahan]

When we say x=0 what about y ? Is it any real number, and what about the equivalence between xy=0 and ( x=0 or y=0)

[faditahan]

What about x=y=0 and why all math people avoid mentioning it, it could be the case