Three methods of proving propositions

To prove a proposition, the general steps are as follows: (1) Draw a graph according to the meaning of the topic; (2) Distinguish the conclusion of propositional conditions, write the topic in the "known" item and the conclusion in the "verified" item in combination with imprisonment; (3) In the item of "proof", write all the reasoning processes.

synthetic method

Using known conditions and some mathematical definitions, axioms, theorems, etc. After a series of reasoning and argumentation, the conclusion to be proved is finally deduced.

analyse

Starting from the conclusion to be proved, we gradually seek the sufficient conditions for its establishment, until finally, the conclusion to be proved is reduced to judging an obviously established condition (known conditions, theorems, definitions, axioms, etc.). ).

reductio ad absurdum

Assuming that the original proposition is not established, through correct reasoning, the contradiction is finally drawn, which shows that the hypothesis is wrong, thus proving the original proposition is established.