1) is a proposition and principle that has been tested by human long-term practice and needs no other judgment to prove.

2) Deduct the initial proposition of the system. Such a proposition does not need to be proved by other propositions in this system, and it is the basic proposition to deduce other propositions in this system.

Theorem:

1. Starting from the true proposition [1] (axiom or other proven theorems), a proposition or formula that is proved to be the correct conclusion through deduction constrained by logic, such as "the opposite sides of a parallelogram are equal" is a theorem in plane geometry.

Generally speaking, in mathematics, only important or interesting statements are called theorems, and proving theorems is the central activity of mathematics. A mathematical statement that is considered true but not proved is a conjecture. When it is proved to be true, it is a theorem. It is the source of the theorem, but it is not the only source. A mathematical statement derived from other theorems can become a guessing process and an unproven theorem.

Inference:

"Inference" is to find a group from a series of examples. When the testee can extract concepts or program knowledge from a series of examples by registering related attributes and noticing the relationship between examples. The process of reasoning includes: comparing examples, identifying group rules, and using group rules to generate new examples that meet group rules.

The so-called "inference", also known as "inference", refers to the thinking process or thinking form of drawing a new proposition from one or several known propositions. Among them, the known proposition is the premise, and the obtained proposition is the conclusion.

Explain the relationship between them in the most popular words:

1, axioms are some obvious and acceptable propositions, but they cannot be proved.

Any mathematical discipline is based on one or several axioms. For example, plane geometry is based on three axioms, one of which is: you can do it after two points, and you can only do a straight line. This can't be proved, it can only be regarded as an axiom. Of course, as a discipline, axioms should be as few as possible.

2. Definition is regulation. In order to learn mathematics conveniently, the language is interlinked, some concepts, nouns, symbols, etc. It must be stipulated. This is the definition. Here, we often see some people say very unprofessional things and even confuse concepts. These people don't have the same language as those who study mathematics, so many questions can't be explained clearly. Last time, there was a person here who didn't even know the concepts of extreme value and extreme value, and didn't want to ask others humbly. Such people have to let him go.

3. Theorem is a proved proposition, which can be used in future math learning and dealing with math problems (such as solving problems). How well a math subject is learned depends largely on the familiarity with theorems.

Inference is also a theorem. If a conclusion is very easy to get from the conclusion of a theorem, it is often written as an inference of this theorem.