2
$\begingroup$

This is a noob question, but I can't quite get my head around this. Suppose I have a set $A = \{\{a, b\}, x, y\}$, how would you go about getting the power set $P(A)$?

Do you go into subset $\{a, b\}$ recursively, or do you treat $\{a, b\}$ as a single element of set $A$?

In other words: would

$P(A)$ = $\{\emptyset, \{\{a,b\}\}, \{x\}, \{y\}, \{\{a,b\},x\}, \{x,y\}, \{\{a,b\},y\}, \{\{a,b\},x,y\}\}$

be correct?

  • 1
    This is a math question, and belongs in math.se. – 2017-01-19

1 Answers 1

2

The powerset of a set $A$ consists of all subsets of $A$, just as in your example.

In the pure form of set theory, there are no "atoms" at all – every set is composed eventually of sets. The transitive closure of a set, which is similar to your "recursive powerset", is important in pure set theory for technical reasons. But it is not commonly used outside of set theory.