Can you explain the differences between true propositions, definitions, theorems, and basic facts with specific examples?

A proposition is a term in mathematical logic, a statement that can be judged to be true or false, usually a declarative sentence. If the statement can first be judged to be true or false, and secondly, it is judged to be true, it is called true. proposition. For example: Beijing is in China, 1+1=2 - it is a proposition, and it is a true proposition; while New York is in Beijing, and the moon is in China, it is a false proposition.

Definition is the abstraction of the connotation of a concept, also known as "definition". For example: force is the effect of an object on an object, radian is the central angle subtended by an arc length of unit length in a unit circle, and so on.

A theorem is a correct proposition. In mathematics, the authenticity of a theorem is derived through logical argumentation based on axioms or other known correct propositions. In physics, theorems are derived from laws (similar to axioms in mathematics) combined with mathematical tools.

Basic facts are basic facts - in fact, not all A's can be further explained.

When people ask questions, the usual approach is: What is A (concept)? Using a language (mathematical, physical, scientific) to reveal, explain, and give a clear definition to A - this is to "define" A; however, not all concepts can be expressed in simpler and more basic terms. It is explained by concepts. Some concepts themselves are already the most basic and simple. For example, if you ask me "what is a point"? "What is a moment?", without any other, I can only answer "a point is a point, a moment is a moment", so for those concepts of "A is A", they are also called meta-concepts in mathematics, which are other basic units that conform to the concept.

The so-called difference is that we know how these are different. In order to do this, we define and define them. If we do this, we will achieve our goal.