Is there such thing as set of empty set?

Question

While I'm reading Is an empty set equal to another empty set?, I wonder if {∅} = ∅?

And it leads to my doubts : is there such things as "set of empty set" with notation {∅}?

If so, then {∅} = ∅?

Related / possible duplicates: Is ${∅}$ an empty set?; Differences in $\varnothing$, {$\varnothing$}, and $\subseteq$; $\emptyset={{\emptyset}}$ — epimorphic, Oct 02 '15 at 08:24
well, I apologise for not searching thorough enough. Obviously the magic keyword ∅ is so much harder to hit than "empty set" ... — user2829759, Oct 02 '15 at 08:27

score 5 · Answer 1 · edited Oct 02 '15 at 08:10

5

$\{\emptyset \}$ has one element, while $\emptyset$ has $0$ elements.

edited Oct 02 '15 at 08:10

answered Oct 02 '15 at 07:58

user300

1,669

score 4 · Accepted Answer · answered Oct 02 '15 at 08:16

4

Think of a box. Empty set is like an empty box. But a box with another box inside it is no longer empty.

answered Oct 02 '15 at 08:16

Ivan Neretin

13,429

I used to understand empty set as "nothing". So "Nothing of nothing" is still "nothing". That was my thinking. While understanding empty set as empty box everything makes sense. So "empty set" shouldn't be "nothing" at all? – user2829759 Oct 02 '15 at 08:23
That's right, it shouldn't. It's a box with nothing inside it. – Ivan Neretin Oct 02 '15 at 08:36

score 2 · Answer 3 · answered Oct 02 '15 at 08:30

2

In your language, the empty set can not be "nothing at all" since it is really a mathematical object: a set with no elements, as you understood thanks to the box example. The fact it does not contain anything does not affect the fact it is a set.

answered Oct 02 '15 at 08:30

Gabriele

141

Is there such thing as set of empty set?

3 Answers3