What is the difference between $\bigcup\left\{ \emptyset,\left\{ 1\right\} \right\}$ and $\bigcup\left\{ \emptyset, 1 \right\}$ ?

  • 3
    $\begingroup$ Why you have the union symbol? $\endgroup$ – MonsieurGalois Jan 19 '17 at 23:20
  • 1
    $\begingroup$ The first one is $\emptyset \cup \{ 1 \} = \{ 1\}$ , while the second one is $\emptyset \cup 1= 1$. $\endgroup$ – Crostul Jan 19 '17 at 23:21

Remember that "$\bigcup X$" means "The set of all things which are elements of elements of $X$."


  • If $X=\{\emptyset, \{1\}\}$: there are two elements of $X$; the first has no elements, the second has one element, namely "$1$"; so $1$ is the only element of an element of $X$. So $\bigcup X=\{1\}$.

  • If $X=\{\emptyset, 1\}$: again, the first element has no elements. So the answer is just "The set of all elements of $1$." This is a bit weird at first, but remember that in set theory, $1$ is a set - namely, $1=\{\emptyset\}$. So $\bigcup X=1$.

In general, if $a$ is a set then $\bigcup\{\emptyset, a\}=a$.


This can be easily reduced to, what is the difference between 1 and {1}.

The first is a number, the second is a bag containing the number.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.