How many subsets are in {∅} and {0}?

[angela107]

Homework Statement

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Relevant Equations

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For ${∅}$, I've come to the conclusion that there is only one subset because it has the empty set and itself as subsets. In this case, there are the same thing.

For ${0}$, there should be two subsets; the empty set and the set itself.

Am I right?

 

[member 587159]

$\{\emptyset\}$ has $\emptyset$ and $\{\emptyset\}$ as subsets and they are not equal. So you are not correct.

 

[angela107]

$\{\emptyset\}$ has $\emptyset$ and $\{\emptyset\}$ as subsets and they are not equal. So you are not correct.

I see. There are two subsets; $∅$, and the subset itself.

 

[PeroK]

I see. There are two subsets; $∅$, and the subset itself.

This is an example where you must think logically rather than practically. There is a difference between "the empty set", denoted by $\emptyset$ and "the set containing the empty set as the only element", denoted by $\{\emptyset \}$.

A non-mathematician might claim that in both cases you have precisely nothing. But, mathematically, they are not the same thing.

 

[mathwonk]

In both cases you hve a set with one element, hence there are two subsets, the subset containing that element and the one not containing it. It does not matter what the element is.