1. A proposition can be a problem, a condition or a conclusion, but they must be clear, concrete and can be solved mathematically. In mathematics, propositions are usually expressed as statements or sentences, and their true and false values can be judged according to their internal logical relations. If a proposition is true, it is called a true proposition; If it is false, it is called a false proposition.
2. According to the true and false propositions, there are true propositions and false propositions. According to the structure of proposition, it can be divided into simple proposition and compound proposition. A simple proposition is a proposition composed of an independent sentence, while a compound proposition is a compound sentence composed of multiple simple propositions.
3. According to the forms of propositions, there are logical equivalent propositions and non-logical equivalent propositions. Logical equivalence proposition means that two propositions are logically equivalent, and non-logical equivalence proposition means that two propositions are not logically equivalent.
4. In mathematics, propositions are widely used, such as geometry, algebra, analysis and other fields. By studying the nature and structure of propositions, we can deeply understand the essence and laws of mathematics, and thus better solve various mathematical problems.
Function of proposition
1. Describe a mathematical problem: a proposition is usually used to describe a mathematical problem or phenomenon. They provide information about problems in a clear and definite way, so that readers can understand the content and requirements of the problems.
2. Provide problem-solving guide: Proposition can provide basic steps and strategies for solving mathematical problems. They not only tell us what kind of problems to solve, but also provide us with methods and ideas to solve them.
3. Establishing knowledge system: In mathematics, proposition is the basis of establishing knowledge system. They not only support new knowledge points, but also help us to understand and connect different mathematical concepts and theories.
4. Promoting mathematical thinking: The process of reasoning and proving propositions is the key to cultivating mathematical thinking. Through analysis, reasoning and argumentation, exercise your logical thinking and ability to analyze problems.
5. Apply to real life: The propositions in mathematics are not only useful in the academic field, but also can be applied to real life. For example, some propositions in geometry can help us solve problems in architecture, engineering and design.