# Isn’t it absurd to suppose that sets can be empty or can contain other sets?

## Do all sets contain the empty set?

The set A is a subset of the set B if and only if every element of A is also an element of B. If A is the empty set then A has no elements and so all of its elements (there are none) belong to B no matter what set B we are dealing with. That is, the empty set is a subset of every set.

## Can a set contain another set?

Can a Set Contain Another Set as an Element? A set can contain other sets as its elements. For example: {{5, 28}} This is a set containing one other set: {5,28}.

## Why do we consider empty set as set?

The empty set is a subset of any set. This is because we form subsets of a set X by selecting (or not selecting) elements from X. One option for a subset is to use no elements at all from X. This gives us the empty set.

## Can there be more than one empty set Why?

In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements. As a result, there can be only one set with no elements, hence the usage of “the empty set” rather than “an empty set”.

## Is the empty set disjoint with other sets?

The empty set is disjoint with itself: ∅∩∅=∅

## Is empty set an invalid set?

An empty set doesn’t contain any elements. The cardinal number of empty set is 0 which is fixed and doesn’t change. So, empty set is a finite set. I hope it is helpful.

## Which set are not empty?

A set which does not contain any element is called an empty set and it is denoted by ϕ. ⇒ {x : x is a rational number and x2 – 1 = 0} is not an empty set.

## How many empty sets are there?

There is only one empty set. It is a subset of every set, including itself.