What do you mean in mathematics: property, judgment, decision theorem?

Nature is what is known or what is known as the object; The decision theorem is to determine whether or not to derive the required conditions for this object.

These are all geometric concepts.

A property refers to a property of a geometric figure, for example, the stability of a triangle is a property of a triangle.

Judgment is the process used to determine the type of a certain figure or the relationship between several figures, for example, the process of proving that a triangle and another triangle are congruent is to determine whether the two triangles are congruent.

The decision theorem is used to directly determine the type of a certain figure or the basis for the relationship between several figures, as long as the conditions of the decision theorem are met, the conclusion of the decision theorem can be reached. For example, one of the theorems about two triangles is that if all three sides of two triangles correspond to the same, then the two triangles are congruent.

That is, as long as we can show that the three sides correspond equally, we can conclude that the two triangles are congruent. This is a judgment that can be directly used to prove the congruence of any two triangles.

What are the conditions for properties in mathematics? Judgment, the judgment theorem is to meet certain conditions, and the judgment leads to a conclusion. For example, two triangles.

The two corners are equal, and the two triangles are congruent. This theorem is the congruence theorem of triangles. The reverse is nature.

Judgment theorem: It is a theorem that determines whether the thing under discussion conforms to a certain concept (or axiom, mathematical saying), and the judgment theorem is a sufficient condition to satisfy a certain concept (axiom), so the main function of the judgment theorem is to judge.

The conditions summarized by the predecessors provide the basis for solving the problem loss.

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Definition: Originally refers to a clear description of the value of a thing. Modern Definition:

a precise and concise description of the essential characteristics of a thing or the connotation and extension of a concept; or to describe or standardize the meaning of a word or concept by listing the basic properties of an event or an object; The defined transaction or object is called the defined item, and its definition is called the defined item.

For example, the definition of a parallelogram: two sets of quadrilaterals with opposite sides parallel to each other, theorem: is a statement that has been proved true by logical limitations. Generally speaking, in mathematics, only important or interesting statements are called theorems. Proving theorems is a central activity in mathematics.

The properties and judgments of the figure are both theorems, properties: the form of things that are recognized from an objective point of view, and in a broad sense: properties are the connection between one thing and other things [if one thing can change one thing, then the two things are related].

For example, the properties of parallelograms: the opposite sides are parallel, the opposite sides are equal, the diagonals are bisected with each other, and the center is symmetrical.

What does it mean to determine the properties of inference in mathematics? Do I have this, do you not have this in your math book?

The simplest example is that the inner wrong angles are equal and the two straight lines are parallel, which is the judgment, and the two straight lines parallel and the inner wrong angles are equal is the property.

1. Assertive theorem: Yes.

to determine whether the thing under discussion at the source conforms to a theorem of a certain concept (or axiom, mathematically speaking), a theorem is a sufficient condition for satisfying a certain concept (axiom), so the main function of a theorem is to judge.

2. Property theorem: It is a theorem obtained from concepts (axioms). The property theorem can be derived directly from the concept (axioms), and when discussing a concept, it contains all its properties, so the main function of the property theorem is to describe.

There is a difference in the conditions given.

1. The theorem is applicable to judging whether the nature of the thing in question conforms to a certain concept.

2. The property theorem is to deduce concepts based on the given properties.

A decision theorem is that a known parallel or perpendicular is extrapolated to other outcomes, and a property theorem is a conditional extrapolation of parallel or perpendicular results.

Differences in the properties, definitions, theorems of mathematics:

1. Mathematical properties: It is the characteristic of mathematical appearance and intrinsic, the property of a thing that distinguishes it from other things.

For example, the two inner angles of an isosceles triangle are equal.

2. Definition of mathematics: Mathematics is a precise and brief explanation of the essential characteristics of a thing or the connotation and extension of a concept.

For example, a triangle with two equal sides is called an isosceles triangle.

3. Mathematical theorems: Theorems refer to propositions that are proved on the basis of existing propositions, which can be other theorems or widely accepted statements, such as axioms.

For example, the determination theorem that the line and surface are perpendicular: if the straight line is perpendicular to two intersecting straight lines in the plane, then the straight line is perpendicular to this plane.

Definition in mathematics is an artificially broad, universal explanatory meaning; a precise and concise description of the essential characteristics of a thing or the connotation and extension of a concept; or to describe or standardize the meaning of a word or concept by listing the basic properties of an event or an object; The defined transaction or object is called the defined item, and its definition is called the defined item. For example, the mathematical definition of a rectangle is: a parallelogram with all four corners at right angles is called a rectangle.

Properties in mathematics refer to the characteristics of the defined terms in the definition. For example, the properties of the rectangle are:

The two diagonal lines are equal;

The two diagonals are bisected with each other;

The two sets of opposite sides are parallel to each other;

The two sets of opposite sides are equal;

All four corners are right angles;

There are 2 axes of symmetry (4 for squares);

It is unstable (easily deformed).

Definition = what this thing is. Nature = what are the properties of this thing. Theorem = how to use this thing.

Definition: A precise and concise description of the essential characteristics of a thing or the connotation and extension of a concept.

Theorem: A statement that has been proved true by logical limitations.

Axiom: refers to basic facts that are self-evident according to human reason.

Concept: In the process of cognition, human beings rise from perceptual cognition to rational cognition, abstracting and summarizing the common essential characteristics of the things they perceive, which is an expression of the cognitive consciousness of the self.

Nature: The connection of one thing to another.

A concept is a representation of a thing, much the same as a definition, and a theorem is a more commonly used equation or formulation derived from an axiom or a proven theorem. The law is the regulation, and the nature is the deeper expression of the food that is introduced by the concept.

Definition – A proposition that is used to mediate something of a certain nature. For example, "A triangle with two equal sides is called an isosceles triangle."

Nature – the property of a thing that distinguishes it from others. For example, "The two inner angles of an isosceles triangle are equal".

Theorem - A proposition or formula that has been proven to be correct and can be used as a principle or law. For example, "two triangles with equal internal angles are isosceles triangles".

According to the use of the theorem, there can be a property theorem, a decision theorem, for example: "a straight line perpendicular to the plane" is defined as "a straight line perpendicular to the plane using a straight line" is called a straight line perpendicular to the plane.

The property theorem that lines are not perpendicular: two straight lines perpendicular to the same plane are parallel to each other.

The determination theorem that lines and planes are perpendicular to two intersecting lines in a plane, then the straight line is perpendicular to this plane.

Theorem: 1. A proposition or formula that starts from a true proposition (axiom or other proven theorem) and proves to be a correct conclusion through deductive deduction limited by logic, for example, "the opposite sides of a parallelogram are equal" is a theorem in plane geometry.

2. Generally speaking, in mathematics, only important or interesting statements are called theorems, and proving theorems is the central activity of mathematics. The number of rents that are believed to be true but not proven is described as conjecture, and when it is proven to be true, the fight is the theorem. It is theorem's, but it's not the only one.

A mathematical narrative derived from other theorems can become a theorem by the process of becoming a conjecture without proof.

As mentioned above, theorems require certain logical frameworks that in turn form a set of axioms (axiom systems).At the same time, a process of reasoning that allows new theorems and other previously discovered theorems to be derived from axioms.

In propositional logic, all proven narratives are called theorems.

Definition: A definition is a description or specification of the meaning of a word or a concept by listing the basic properties of a thing or an object. The thing or object that is defined is called the defined term, and its definition is called the defined term.

For example, in the definition of "a bachelor is an unmarried man", "bachelor" is the defined term, and "unmarried man" is the definition term. The "a" and "is" in the definition can be replaced by symbols, such as using the symbol :=, and the above definition can be transcribed as:

Bachelor: = unmarried man".In general, a definition, like the example above, is often a sentence that expresses the equivalence between the defined term and the defined term.

Nature: The nature of the thing itself as distinct from that of other things: The nature of the problem The editorial is of a guiding nature.

Nature is the essence of things.

Judgment: Judging things based on certain facts.

<>1. Definition is a precise and concise explanation of the essential characteristics of a thing or the connotation and extension of a concept, or to describe or standardize the meaning of a word or a concept by listing the basic properties of an event or an object;

2. The judgment is to give one's own opinion on the late answer question that has not yet reached a conclusion. The definition is biased towards explaining the essential characteristics of a thing, and the judgment is a subjective judgment of a thing.