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I'm struggling to understand what the double {{}} means

Trevor Gunn
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Matheus Ribeiro Marinho
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    There are so so many questions on this site about sets of sets of sets, sets of empty sets, which are subsets of what, etc. – Trevor Gunn Apr 30 '22 at 23:47

3 Answers3

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The first is false (because $\emptyset$ is not an element of $\{\{\emptyset\},1\}$); the second is true. The double $\{\{\emptyset\}\}$ means "the set containing the set containing the empty set".

TonyK
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$\emptyset$ is the set with no elements, $\{\emptyset\}$ is the set whose only element is the set with no elements, and $\{\{\emptyset\}\}$ is the set whose only element is the set whose only element is the set with no elements, so $\{\emptyset\}\in \{\{\emptyset\}\}$ as an element

Guillermo García Sáez
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$\{...\}$ means the set whose members are all those and only those things that are equal to anything named, listed, described, or defined by the "$...$".

$\{\emptyset\}$ is the set whose sole member is $\emptyset$.

If the "$...$" is "$\{\emptyset\}$" then we have $\{\{\emptyset\}\}$ which is a set whose sole member is $\{\emptyset\}$.

Some beginners have difficulty in accepting that a set may be a member of another set

DanielWainfleet
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