1

What does the following set notation mean:

$$\{\{1\},\{2\}\}$$

What are the elements or subsets of this set?

Is this the same as $\{1,2\}$?

What about $$\{\{1\}\}$$ ?

mavavilj
  • 7,270
  • 6
    No, it is not. The elements of the set ${{1},{2}}$ are the sets ${1}$ and ${2}$; the elements of the set ${1,2}$ are the integers $1$ and $2$. – Brian M. Scott Nov 01 '16 at 18:32
  • @BrianM.Scott What about the empty set? – mavavilj Nov 01 '16 at 18:34
  • What about it? It’s not an element of either of these sets, though of course it is a subset of both. – Brian M. Scott Nov 01 '16 at 18:37
  • Related http://math.stackexchange.com/questions/258891/is-the-set-1-emptyset-a-subset-of-1, http://math.stackexchange.com/questions/638560/why-can-a-1-element-set-be-a-member-of-another-set-but-not-a-subset-of-it – Ethan Bolker Nov 01 '16 at 19:04

2 Answers2

2

$\big\{\{1\},\{2\}\big\}$ means the set that contains $\{1\}$ and $\{2\}$. It's in no way the same as $\{1,2\}$ which contains $1$ and $2$, and not $\{1\}$ and $\{2\}$.

Workaholic
  • 6,763
2

The elements of the set $\{\{1\},\{2\}\}$ are $\{1\}$ and $\{2\}$. It is not equal to $\{1,2\}$.

adjan
  • 5,741