Natural numbers can be represented as
$0=\emptyset$
$1=\{\emptyset\}$
$2=\{\{\emptyset\}\}$
$...$
or as
$0=\emptyset$
$1=\{0\}=0\cup\{0\}$
$2=\{0,1\}=1\cup\{1\}$
$...$
What are the names of these representations?
Aren't they identical?
What are advantages of second representation?