What is the definition of a proposition?

In mathematics, definitions, axioms, formulas, properties, laws and theorems are all mathematical propositions. We usually call statements that can be expressed by language, symbols or formulas within a certain range and can be judged to be true or false as propositions.

The definition of propositions The definitions, axioms, formulas, properties, laws and theorems in mathematics are all mathematical propositions. These are the basis for judging whether the proposition is true or false through reasoning. Generally speaking, in mathematics, we call statements that can be expressed in language, symbols or formulas within a certain range and can judge whether they are true or false as propositions.

Proposition classification 1. Original proposition: A proposition itself is called the original proposition. For example, if x> 1, then f(x)=(x- 1) 2 monotonically increases.

2. Inverse proposition: a new proposition that reverses the conditions and conclusions of the original proposition. For example, if f(x)=(x- 1) 2 monotonically increases, then x >；; 1。

3. No proposition: a new proposition that completely negates the conditions and conclusions of the original proposition, but does not change the order of conditions and conclusions. For example, if x≤ 1, then f(x)=(x- 1) 2 is not monotonically increasing.

4. Negative proposition: A new proposition that reverses the conditions and conclusions of the original proposition, and then completely negates the conditions and conclusions. For example, if f(x)=(x- 1) 2 is not monotonically increasing, then x≤ 1.

The difference between definition and proposition is the cognitive behavior that the cognitive subject uses the linguistic logic form of judgment or proposition to determine the position and boundary of an object or thing in the comprehensive classification system of related things, so as to make this object or thing stand out from the comprehensive classification system of related things.

The concept of proposition is a phenomenon that can be defined and observed. Proposition refers not to the judgment (statement) itself, but to the semantics expressed. When different judgments (statements) have the same semantics, they express the same proposition.

In other words, the definition is artificially defined, the proposition is a judgment sentence, the proposition is true or false, and the definition is not.