(1) Are axioms and theorems true propositions? What's the difference between them? (2) What is proof? What are the steps to prove a geometric proposition? (3) How to judge whether a proposition is false?

(1) Are axioms and theorems true propositions? What's the difference between them? (2) What is proof? What are the steps to prove a geometric proposition? (3) How to judge whether a proposition is false?

1. Axioms are summed up and cannot be proved. Theorems are derived from axioms and can be proved. They are all true propositions
2. Proof is to deduce propositions from basic axioms and theorems
3. A counterexample proves the false proposition

The theorem is obtained from axiom or other true propositions by logical reasoning（
Fill in the blanks

In the space is "conclusion",

The relationship between true proposition and false proposition and theorem and axiom
Please make it clear

Axioms are fundamental That is to say, it can be accepted and believed by people without special proof A theorem is a correct theory proved by reasoning based on kilometers
The true proposition is the correct one, and the latter is the incorrect one Then the relationship between the two It's the relationship between right and wrong

If a > b, then a + b > b + C, the axioms and theorems involved in this proposition are?
The wrong number is a + C > b + C

Is the basic property of inequality, called additivity
Other properties:
Property 1: if a > b, b > C, then a > C (transitivity of inequality)
Property 2: if a > b, then a + C > b + C (additive inequality)
Property 3: if a > b, C > 0, then AC > BC; if a > b, CD, then a + C > b + D
Property 5: if a > b > 0, C > d > 0, then AC > BD