Mathematics, about sets, what is sets in mathematics

1. Any element x belongs to m, so that x=a+1 6, a z is x=(2a+1) 2+1 3

where 2a + 1 z

Then x belongs to n, and any element in m belongs to n, that is, m contains any element x in n belongs to n....In the absence of this relation, then m is really contained in n2, and any element x belongs to n, so that x=a 2-1 3 and a z is x=(a-1) 2+1 6

of which A-1 Z

Then x belongs to p, and any element in n belongs to p, i.e., n is contained in p, and in the same way, p is included in n

That is, n = p sum up, m is really contained in n, n = p

All points. m=;

n=; p=;

For 3n-2, it is equal to 3n+1, so n=p contains m

m is included in p, and n is included in n, and the common ground is found first.

Comparison of m and p 2 shows that m is included in p

Then 1 3 and 1 6 are compared, and p is included in n

See if it's included or included.

x = + inverse proportional function y=2 x is the set of values that can be taken by x.

The collection is generally.

In the first year of high school.

The foundation of mathematics.

Chapter. Be. High School Mathematics.

The basics of functions

About the concept of collections:

Concepts such as points, lines, and surfaces are all of them.

Primitive in geometry, without addition.

defines the concept of a set is.

The primitive, undefined concept of set theory.

Middle school algebra. has known "sets of positive numbers" and "sets of solutions of inequalities"; In junior high school geometry, it is also known that the perpendicular line is "the set of points at equal distances to two fixed points" and so on. When it comes to getting started with the concept of collections, it's mostly through.

Examples, to have a preliminary understanding of the concept. The textbook gives "in general, certain specified sets of objects."

Together it becomes a set, also referred to as a set. That's just right.

Collection concept. Descriptive description.

We can cite a lot.

Reality in life.

examples to further illustrate this concept, thus clarifying that the concept of sets is like any other.

Mathematical concepts. The same, not something that people imagine out of thin air, but from it.

The real world. In summary, a set: A set of specified objects that come together to form a set.

The representation of the collection.

1. Enumeration method: list the elements in the set one by one and write them in.

A method that represents a collection in curly braces.

For example, by equations.

The set of all solutions can be expressed as.

Note: (1) Some sets can also be represented as follows:

A set of all integers from 51 to 100:

A set of all positive odd numbers:

2) A is different from a: a denotes an element, denotes a set, and the set has only one element.

Descriptive: A method that indicates whether certain objects belong to the set with a definite condition, and writes this condition in curly brackets to indicate the set.

Format: Meaning.

A set of x that satisfies the condition p(x) in set a.

For example, inequalities.

The set of solutions can be expressed as: or all.

Right-angled triangle.

The set of can be expressed as:

Note: (1) In the case of no confusion, the vertical line and the left part can be omitted.

As:; (2)

Misrepresentation:;

3. Venn Diagram: A method of representing a set with the inside of a closed curve.

Note: When is the enumeration method used? When to use descriptive?

1) The common attributes of some sets are not obvious, difficult to generalize, and inconvenient to be expressed by description, so they can only be expressed by enumeration.

2) Some elements of the set cannot be listed one by one, or it is inconvenient and does not need to be listed one by one, and the description method is commonly used.

Such as: Collection.

"Set" is a basic concept in mathematics, and it is also the main research object of set theory. The basic theory of set theory was created in the 19th century, and the simplest way to say about a set is the definition in naïve set theory, that is, a set is "a definite set of things", and the "things" in a set are called elements.

Set has incomparable special importance in the field of mathematics, the foundation of set theory was laid by the German mathematician Cantor in the 70s of the 19th century, after a large number of scientists for half a century of efforts, by the 20s of the 20th century has established its basic position in the system of modern mathematical theory, it can be said that almost all the achievements of various branches of modern mathematics are built on strict set theory.

7 pcs. Here's the idea.

Because 1 5 6, 2 4 6, 3 3 6

So the number in s must be 1 and 4 at the same time, and 3 can appear separately.

So the number is 1 (with one number) 2 (with two numbers) 2 (with three numbers) + 1 (with four numbers) 1 ({1,2,3,4,5) with five numbers) 7

The first problem can draw a number line, and then mark the area of the A set, and then B is the second problem of X, because the two sets are equal, that is, the two sets have the same elements, and the set on the right has 0, that is, either a=0, or a+b=0

If a=0, then the right set b a has no meaning, so it can only be a+b=0, and then the left set has 1, so either b=1 or b a=1, b=1, then a=-1, and the equation holds. If b a=1, then a=b, but a+b=0, so a=b=0, but there can't be the same elements in the set, so this can't be, so it's b=1, a=-1

In fact, drawing a venn diagram is the best way to understand both.