# can the empty set contain itself? [duplicate]

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: $$\emptyset \supseteq \{ \emptyset \} \Rightarrow \emptyset = \{ \emptyset \}$$.

## marked as duplicate by Mauro ALLEGRANZA, Community♦May 20 at 18:51

• 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. – Mauro ALLEGRANZA May 20 at 18:51