# Is zero an element of the empty set?

I have a question about the empty set.

Is $0$ (zero) an element of $\varnothing$? And what is the cardinality of {0}?

• The empty set has no elements.
– Dirk
Oct 27, 2016 at 19:27
• Perhaps you should repeat in high voice the definition of the "empty set" ... Oct 27, 2016 at 19:28
• The cardinality of $\{0\}$ is $1$.
– user228113
Oct 27, 2016 at 19:28
• Funny enough, some set theorists may say that $\{0\}$ actually is $1$ (and that $0=\emptyset$).
– user228113
Oct 27, 2016 at 19:30
• @G.Sassatelli Most probably those set theorists would also give a set up of assumptions, axioms, etc. in which that would make some sense....or they are high, of course. :) Oct 27, 2016 at 19:31

You have two boxes separate from each other. One box contains nothing. The other box has a piece of paper with the number zero on it. The first box represents $\{ \} = \emptyset$ while the second represents $\{ 0 \}$. Two different things. The first has no objects, the second has only one.
• @fleablood Look at it this way: The set of all integers less than 1 and greater than -1 is $\{0\}$. The set of all integers greater than 1 and less than 2 is $\emptyset$. The two are not the same thing. Oct 27, 2016 at 19:39