Whoever helps me summarize the empty set, it should contain various types of questions

The definition of an empty set is a set that does not contain any subsets, that is to say, an empty set cannot contain an empty set, but in the latter, an empty set is an element in the set, so it can be said that it contains an empty set.

Representation: Symbols or representations.

Note: There is a collection of elements, not an empty set.

In latex, an empty set means emptyset.

0 is a number, not a set.

It's a set, and the set has only 0 elements.

is a collection, but does not contain any elements.

is a non-null set, and the set has only the element of the null set.

RelevanceFor any set a, the empty set is a subset of a: a: a.

For any set a, the union of the empty set and a is a: a:a a.

For any non-null set a, the null set is a true subset of a: a,,, if a≠ then true is contained in a.

For any set a, the intersection of the empty set and a is an empty set: a, a is an empty set for any set a, the Cartesian product of the empty set and a is an empty set: a, a

To say what I understand:

No, the former should be right, which is like {1} contained in the {1}, and the same set is a subset of each other;

The latter should be wrong, an empty set is a set without any elements, and {empty set} is a set of "empty sets" as elements, and it should be correct to say that "empty sets belong to {empty sets}".

No, an empty set has no elements, and {empty set} has an element: an empty set.

Both are true, because the answer is this.

The former is certainly true, because an empty set is a subset of an arbitrary set, and this arbitrary set can refer to the empty set itself. The latter is even more true, because the empty set cannot belong to the empty set, that is, there are no elements in the empty set. It is necessary to distinguish between the relationship of inclusion and belonging.

"An empty set is a subset of any set" is a true proposition.

An empty set is a collection that does not contain any elements and is a subset of any collection, a true subset of any non-empty collection. An empty set is not none; It is a collection with no elements inside. Empty sets are represented by symbols or symbols.

Note: 1. There is a collection of elements, not an empty set.

It's a number, not a set.

3. It is a set, and the set only has the element of 0.

4. It is a collection, but does not contain any elements.

5. It is a non-empty set, and the set only has the element of an empty set.

There is no subset of empty sets; Error A subset of an empty set is itself Any set has at least two subsets; Error Empty set has only one subset An empty set is a true subset of any set; Error An empty set is a true subset of any non-empty set If an empty set is really contained in set a, then a ≠ empty set is correct

Yes, first you have to understand what an empty set is and what a subset is. Regarding subsets, for example, there are many elements in a set A, and then all the elements in set B can be found in A, so B is said to be a subset of A. You can think of A as a piece of territory, and then B's territory is completely inside A, so B is A's grandson.

And the empty set is that there is no territory, and anyone can call it grandson.

It's a true proposition.

An empty set is also a true subset of any non-empty set.

1. Overview:

1. Definition of empty set:A collection that does not contain any elements is called an empty set

2. The nature of the empty set:An empty set is a subset of everything set.

An empty set is a true subset of any non-empty set

Second, the way of representation:

1. Representation: use symbols (note: (pronounced oe) is the Latin alphabet, which is different from the Greek alphabet (pronounced fi)) or represented.

2. Note: There is a set of (oe) elements, not an empty set. Represented as emptyset in latex.

3. Examples:1. When two circles are separated, the set of their common points is an empty set;

2. When the discriminant value of the root of a quadratic equation is less than 0, the set of its real roots is also an empty set.

There is no practical point in discussing empty sets here, so there is no need to write about it.

Empty sets are generally written as subsets, depending on the problem.

This is a set, and when you ask for its subset, write the empty set into it.

Inside a set is an element, while an empty set is a set.

An empty set is a collection that does not contain any elements. An empty set is a subset of any set and is a true subset of any non-empty set. An empty set is not none; It is a collection with no elements inside.

Think of a set as a bag with elements, and the bag of an empty set is empty, but the bag itself does exist.

For example, the intersection of sets a=, sets b=, and sets a and set b is an empty set.

1 There is a sentence in all, I don't know if the teacher said it when you learned to gather, I remember that it was said in the book, and maybe it was not said in the book, but this sentence is right. "An empty set is a subset of any set, and an empty set is a true subset of any non-empty set. Then the natural empty set is contained in the empty set.

A friend said earlier, "If you look at it as a set relationship: you can also say: Contained in Here is a conceptual mistake, if you discuss the relationship between the two, you can't say "really contained in Because the former is an element and the latter is a set, it should be used to belong, not contain."

Why do we stipulate that "an empty set is a subset of any set, and an empty set is a true subset of any non-empty set." (hereinafter ** on the Internet).

Any algebraic system must contain zero elements, which are immovable elements of addition, that is, for any element a in this algebraic system, there must be an element o, so that a+o=o+a=a=a.

In an algebraic system composed of real numbers, the number 0 is the zero element;

In an algebraic system composed of vectors, a zero vector is a zero element, so there is a zero vector in any direction;

In the algebraic system composed of matrices, the zero matrix is the zero element, and there is a zero matrix in the whole matrix, no matter how many rows or columns there are;

In an algebraic system composed of sets, the empty set is the zero element, without which the operation between sets cannot be defined, so we must stipulate that the empty set is a subset of any set, and only in this way can we define the operation between sets, so that sets become the object of our mathematical research.

An empty set is a subset of any set that we dictate and cannot be extrapolated from the definition of a subset.

Actually, this is a false assertion.

Personally, I think:

If you think of it as a set relation: True Inclusion in It can also be said that: Contained in specifies that an empty set is a subset of any set, and is a true subset of any non-empty set.

However, an empty set cannot be included in an empty set.

False, an empty set limits itself to a set that has no elements, and if it contains an empty set, it contradicts the concept of an empty set, so this sentence is wrong.

According to the definition of the set and the empty set.

The definition of can be discerned.

a The subset of the empty set is the empty stove wisdom set, so there is no true subset of the empty set.

So a is correct

b When a set is an empty set, there is only one subset, so B error c An empty set is a subset of any set, a true subset of any non-empty set, so C error D An empty set is a subset of any set, so D is wrong

So choose A

In the second problem, b is 4x+a 0, and the solution is 4x -a, x -a 4 and no matter what a is, -a 4 is a meaningful number.

So in Pybi and here, Dust Stalking B can't be empty.

Of course, there is no need to consider the case of empty sets.

In the first question, a is k+1 x 2k, if k+1 2k, then x must be larger than the larger number k+1, but smaller than the smaller number 2k, which is of course impossible. So when k+1 2k, a is an empty set.

Therefore, in these two questions, question 1, as a subset of a, may obtain an empty set, of course, it needs to be considered.

Second, he, as a subset of the Hui Bureau, B, cannot obtain an empty set, of course, there is no need to think about it.

That's why empty sets are taken into account or not.

The second question b is not possible to empty the set.