the difference between $\emptyset$ and $\{\emptyset\}$?

Question

What is the difference between $\emptyset$ and $\{\emptyset\}$?

I am reading from some notes and author denotes the empty set by $\{\emptyset\}$. I am getting confused as definition says

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements

I think $\{\emptyset\}$ is wrong notation as that implies that it has one element. More specifically it should be the notation of power set of $\emptyset$

The empty set is not denoted as ${\varnothing}$, but as ${}$ or as $\varnothing$. It contains no elements. This in contrast with ${\varnothing}$ which contains $\varnothing$ as element. — drhab, Oct 13 '18 at 14:42
@AlexKruckman It is the hand written notes which I got from my friend. I am self studying set theory. I can send you the camera picture if you want. — Shweta Aggrawal, Oct 13 '18 at 14:50
@StammeringMathematician Oh, I see. No, you don't need to send me a picture. Maybe it's possible your friend took down the notes incorrectly... — Alex Kruckman, Oct 13 '18 at 14:52

score 1 · Accepted Answer · answered Oct 13 '18 at 14:41

1

$\{\varnothing\}$ is a set containing the emptyset. The other is the emptyset, it does not contain elements.

answered Oct 13 '18 at 14:41

Gibbs

8,230

"..emptyset" or "empti-element" ? – G Cab Oct 13 '18 at 14:43
1

Can you define "empti-element"? – Gibbs Oct 13 '18 at 14:45
@Gibbs I have reached the daily upvote limit. I will upvote the answer later. I appreciate your answer. Thanks for taking your time. Cheers!!! – Shweta Aggrawal Oct 13 '18 at 14:48
@Gibbs: got it, thanks. – G Cab Oct 13 '18 at 14:52

the difference between $\emptyset$ and $\{\emptyset\}$?

1 Answers1