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This question already has an answer here:

This question may sound weird but anyway here it goes. Is the following equation true? $$\emptyset = \{ \emptyset \}$$

The reason I think it is not true:

  • The empty set is an element by itself, therefore the R.H.S contains one element. But due to L.H.S, the amount of elements of the R.H.S must be $0$.

The reason I think it is true:

  • The empty set is a subset of every set. Therefore, the emptyset on the R.H.S must be a subset of the L.H.S. In other words, we have the following relation: $\emptyset \supseteq \{ \emptyset \} \Rightarrow \emptyset = \{ \emptyset \}$.
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marked as duplicate by Mauro ALLEGRANZA, Community May 20 at 18:51

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ No, it is not true. $\endgroup$ – Mauro ALLEGRANZA May 20 at 18:48
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    $\begingroup$ The empty set is empty i.e. has no elements. $\endgroup$ – Mauro ALLEGRANZA May 20 at 18:48
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    $\begingroup$ (Put another way: is an empty bag the same thing as a bag that contains an empty bag inside?) $\endgroup$ – Arturo Magidin May 20 at 18:49
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    $\begingroup$ I did search after this question before I did poste it. Sorry for dublicate @MauroALLEGRANZA. $\endgroup$ – LocalMartingale May 20 at 18:50
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    $\begingroup$ You have to separete $\in$ (is an element of) from $\subseteq$ (is a subset of). You have to use "contain" as a synonym of one of the two, but not both. $\endgroup$ – Mauro ALLEGRANZA May 20 at 18:51
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The empty set contains itself but the empty set is not an element of itself. The set whose only element is the empty set is not the empty set.

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