Question

How do you write mathematical proofs?

Answer 1

Hint:Mathematical proofs in simple terms can be explained as a method to check whether a given mathematical proposition is right or wrong. Such that due to this nature we can say that proofs are fundamental to mathematics.Considering the above facts we can elaborate the method by which we can write mathematical proofs.

Complete step by step answer:
We have to elaborate the process by which we can write mathematical proofs.On analyzing the nature of mathematical proofs we can say that there is no specific formula for writing a proof.We usually begin with the given information and then develop on the basis of that.Also we can take other basic or known facts and include them to prove our point of view.These are essential to get the conclusion for a specific proof.

Now on analyzing the nature of proofs it can be divided into many groups. Some of them are:
Two Column Proofs: Here as the name suggests statements are written in one side of the column and their justifications on the other side.
Flowchart Proofs: Here the statements are written in boxes and justification as arrows connecting the statements.
Proof by contradiction: Here the conclusion is assumed to be false then we have to show that the assumption is false since it contradicts.
Proof by cases: All the possibilities are divided into different cases and then each one is proved separately.

No matter how many types of proofs there are, the general structure of solving a mathematical proof involves starting off with a known statement and then developing from it we should conclude something new.

Note:Depending on the nature of the given statement there may be multiple ways to prove something or no way at all depending on the nature of the system. There are many techniques to make one understand the application of various proof techniques.