Proof Method Analysis

There are many ways to prove mathematics. Today, I think it is classic to turn discrete mathematics into the proof method, so that I can keep them in mind.

The common form of theorem is "P is true when Q is true", and "If P is true, Q is true ". The former is equivalent to P's launch of Q, and Q also releases P. So in the final analysis, the main form of theorem is P's release of Q. As for other forms, such as non-P forms, only proof that P is false, PQ is true, only proof that P is true and Q is true, P or Q is true, only proof that P is true, P is not true.

1. Meaningless proof

If the premise is false, the conclusion is true or false, and the proposition is proved. (If it proves that P is not true, then P launches Q)

2. Proof of ordinary

The proof conclusion is always true, so the premise is true or false, and the proposition must be proved. (If Q is proved to be true, P releases Q)

3. Direct proof

Assuming that the premise is true, the conclusion is established successfully, and the proposition is proved. (If p is set up and Q is set up, P is set up)

4. Indirect proof

Based on the principles of inverse proposition and original proposition equivalence, the original proposition can be proved to be true by proving that the inverse proposition is true. (If Q is not true and P is not true, then Q is true)

5. Multi-precondition proposition

P1, P2, P3,..., PN introduces the Q-form proposition.

Direct proof: If the premise pi is all set up and Q is successfully launched, the conclusion is true;

Indirect proof: If Q is not true and any pi is not true, the conclusion is true.

6. Conditional proposition with multiple preconditions (deduction)

P1, P2, P3,..., PN releases the Q-form proposition of P.

The proposition form is equivalent to that where the multi-precondition Pi has a precondition P, which is no different from P in the precondition. That is to say, the original proposition is P1, P2, P3,..., Pn, P, and the Q form is introduced.

This rule is called deduction theorem.

7. Multiple optional preconditions

Any existence of any of the prerequisites for P1, P2, P3,... and Pn has a proposition in the Q format.

According to its own description, this proposition should prove that any pi can launch Q to ensure that Q is not valid only when the premise pi is not true.

8. Reverse Identification Method

To prove that P1, P2, P3,..., PN always launch Q, you can use another method:

Prove that P1, P2, P3,..., Pn, and non-q always come up with an impossible conclusion. That is to say, we should take the counterproposition of Conclusion Q as an additional premise. At this time, all the premise assumptions will launch a situation that is never possible.