# Is the empty set disjoint with itself?

1. Sep 15, 2009

### CantorSet

My apologies if the following is a stupid question. But is the empty set disjoint with itself? Certain aspects of set theory has always been counter-intuitive for me.

$$\oslash\cap\oslash=\oslash$$?

2. Sep 15, 2009

### HallsofIvy

Staff Emeritus
Yes, it is certainly true that $$\oslash\cap\oslash=\oslash$$.

3. Sep 16, 2009

### g_edgar

If A and B are not disjoint, it means there is some element belonging to both of them. Anyone who claims the empty set is not disjoint from itself must provide us with an element belonging to the empty set!