# Is the empty set disjoint with itself?

#### 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.

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

Related Set Theory, Logic, Probability, Statistics News on Phys.org

#### HallsofIvy

Homework Helper
Yes, it is certainly true that $$\oslash\cap\oslash=\oslash$$.

#### 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!

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving