An empty set is a subset of any set and a proper subset of any non-empty set. Empty set is not nothing; It is a collection with no elements inside. Use symbols? Or {} means. Note: {? } Is there? A collection of elements, not an empty set. In LaTeX, an empty set represents the code \ \emptyset.
0 is a number, not a set. {0} is a collection with only element 0. ? Is a collection, but does not contain any elements. {? } is a non-empty set, and the set has only elements of an empty set. When two circles are separated, the set of their common points is an empty set; When the discriminant value of the roots of a quadratic equation is △ < 0, the set of its roots is also an empty set.
Matters needing attention in calculating empty set
1, an empty set is a special set, indicating that there are no elements. It usually uses symbols? Or {} means.
2. Empty set is an abstract concept in mathematics, so it can't be used in practical calculation. Because there are no elements involved in the operation, most operations cannot be applied to empty sets.
3. In set operation, some properties related to empty sets need special attention. For example, for any set A, there is a ∨? = a and A∩? =? That is, the union of arbitrary set and empty set is still the set itself, and the intersection of arbitrary set and empty set is an empty set.
4. When using empty sets to participate in some specific operations, we should be extra careful to deal with boundary conditions. For example, when finding the power set of a set, the empty set as a special subset needs special consideration.
5. Empty set plays an important role in the fields of set theory and logic, and it is of certain significance to understand the process of set operation and reasoning, but we should pay attention to its particularity when calculating specific problems.