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I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)
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Why every set has an empty set?
Any set has the empty set as subset A is a subset of B if each element of A is an element of B For the empty set ∅ the vacuum property holds For every element of ∅ whatever property holds, also being element of an arbitrary set B, therefore ∅ is a subset of any set, even itself ∅ has an unique subset: itself
Which sets does the number zero belong?
There are an infinity of possible answers: the integers, rationals, reals, complex numbers, the set {0,1,-3}, the set containing only the element 0;
What is the rule of a set of numbers?
The only rule for any set is that given any element [number], you should be able to determine whether or not it is a member of the set.
What is surjective in algebra mapping?
A mapping, f, from set S to set T is said to be surjective if for every element in set T, there is some element in S such that it maps on to the element in T. Thus, if t is any element of T, there must be some element, s, in S such that f(s) = t.
What is inverse in algebra?
Given a set and a binary operation defined on the set, the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation. If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k. If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.
