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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 $\emptyset$


marked as duplicate by Key Flex, ArsenBerk, Matthew Towers, Community Oct 13 '18 at 14:55

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    $\begingroup$ One is the empty set, and the other isn't. $\endgroup$ – Lord Shark the Unknown Oct 13 '18 at 14:40
  • $\begingroup$ 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. $\endgroup$ – drhab Oct 13 '18 at 14:42
  • $\begingroup$ Can you link to the notes you're reading? $\endgroup$ – Alex Kruckman Oct 13 '18 at 14:48
  • $\begingroup$ @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. $\endgroup$ – StammeringMathematician Oct 13 '18 at 14:50
  • $\begingroup$ @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... $\endgroup$ – Alex Kruckman Oct 13 '18 at 14:52

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

  • $\begingroup$ "..emptyset" or "empti-element" ? $\endgroup$ – G Cab Oct 13 '18 at 14:43
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    $\begingroup$ Can you define "empti-element"? $\endgroup$ – Gibbs Oct 13 '18 at 14:45
  • $\begingroup$ @Gibbs I have reached the daily upvote limit. I will upvote the answer later. I appreciate your answer. Thanks for taking your time. Cheers!!! $\endgroup$ – StammeringMathematician Oct 13 '18 at 14:48
  • $\begingroup$ @Gibbs: got it, thanks. $\endgroup$ – G Cab Oct 13 '18 at 14:52

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