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What is the definition for additive identity property of 0?
0 is the identity element of a set such that 0 + x = x = x + 0 for all elements x in the set.
Definition of compact set?
A set S of real numbers is called compact if every sequence in S has a subsequence that converges to an element again contained in S.
Is empty set super set?
No, an empty set can't be the super set.The definition of super set is as follows:If A and B are sets, and every element of A is also an element of B, then B is the super set of A, denoted by B ⊇ A.Another way to interpret this is A ⊆ B, which means that "A is the subset of B".Suppose that ∅ is the super set. This implies:∅ ⊇ A [Which is not true! Contradiction!]Remember that ∅ and {∅} are two different sets. If we have {∅}, then there exists an element that belongs to that set since ∅ is contained in that set. On the other hand, ∅ doesn't have any element, including ∅.Therefore, an empty set can't be the super set.
What is the definition for zero identity property?
The zero identity is defined in the context of a binary operation defined by addition over a set. It states that there is an element in the set, denoted by 0, such that for every element, X, in the set, 0 + X = X = X + 0. Addition in the set need not be commutative, but addition of 0 must be.
What is the definition for identity properties for addition and multiplication?
The identity property for addition is that there exists an element of the set, usually denoted by 0, such that for any element, X, in the set, X + 0 = X = 0 + X Similarly, the multiplicative identity, denoted by 1, is an element such that for any member, Y, of the set, Y * 1 = Y = 1 * Y
