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# Why null set is not considered as an element of any set even though it is an subset of every set?

Wiki User

2009-04-13 10:32:00

Let set A = { 1, 2, 3 }

Set A has 3 elements.

The subsets of A are

{null}, {1}, {2}, {3}, {1,2},{1,3},{1,2,3}

This is true that the null set {} is a subset.

But how many elements are in the null set? 0 elements.

this is why the null set is not an element of any set, but a subset of any set.

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Using the above example, the null set is not an element of the set {1,2,3}, true.

{1} is a subset of the set {1,2,3} but it's not an element of the set {1,2,3}, either.

Look at the distinction: 1 is an element of the set {1,2,3} but {1} (the set containing the number 1) is not an element of {1,2,3}.

If we are just talking about sets of numbers, then another set will never be an element of the set. Numbers will be elements of the set. Other sets will not be elements of the set.

Once we start talking about more abstract sets, like sets of sets, then a set can be an element of a set. Take for example the set consisting of the two sets {null} and {1,2}.

The null set is an element of this set.

Wiki User

2009-04-13 10:32:00
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Q: Why null set is not considered as an element of any set even though it is an subset of every set?