Power set

  • Thread starter Madonna M.
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  • #1
Madonna M.
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1. Homework Statement

How many elements does this set have?

* P(P(∅))

2. Homework Equations

I know that if a set has n elements, then its power set has 2^n elements but i really want to know if (P(∅)) is just one element or not.

Thanks in advance..
 

Answers and Replies

  • #2
jbunniii
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How many subsets does ##\emptyset## have?
 
  • #3
Dick
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1. Homework Statement

How many elements does this set have?

* P(P(∅))

2. Homework Equations

I know that if a set has n elements, then its power set has 2^n elements but i really want to know if (P(∅)) is just one element or not.

Thanks in advance..

Sure it is. The empty set has one subset. Itself. But remember P is the SET of subsets. So P(∅) isn't ∅. It's {∅}. There is a difference.
 

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