# the difference between $\emptyset$ and $\{\emptyset\}$? [duplicate]

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

## 1 Answer

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

• "..emptyset" or "empti-element" ? – G Cab Oct 13 '18 at 14:43
• 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!!! – StammeringMathematician Oct 13 '18 at 14:48
• @Gibbs: got it, thanks. – G Cab Oct 13 '18 at 14:52