Is Zero an element of an empty set.

To understand the zero is an element of an empty set, first we need to understand the difference between the empty set and zero.

Difference between the empty set and zero

For example, we take a set of two parallel lines AB and CD, and they intersect each other at a point P.

But it is not possible because there is no any point where the parallel lines are intersect each other.

So we can say that there is zero number of points where the parallel lines are intersects. So it is a empty set.

If we write it {0} as the answer of this question then it will be wrong because it shows that it has an element but the empty set does not have any element.

So, it must be blank {} and there is no element in the bracket.

Here is the number of element is zero, but zero is not the element of this set.

Example : Odd numbers divided by 2. But it is not possible because there is no any odd number that divide by 2. So it is a empty set.

Example : Even numbers divided by 5. But it is not possible because there is no any even number that divide by 5. So it is a empty set.

Example : A = {0, 2, 4, 6, 8}

Here set A has 5 elements and 0 is one of the element of the set.

In above set A, if we find subset of set A, we write {0} as the subset of the set A.

In this case it is not an empty set. It contains one element in it.

But we also know that empty set is the subset of every set, so, {} is also the subset of A.

So {0} and ∅ or {} are the subset of A, but both are not same.

Note: Zero is the number of element in empty set, not the element of empty set.