A proof is a mathematical argument that shows that something is absolutely true, without a doubt. Mathematicians begin their process of mathematical inquiry by suggesting that something might be true. This is called a conjecture. Then they must prove that it is true all the time.
Certainty in mathematics is vital and it's one of the aspects that students most love about the subject. Either it's right or it's wrong. Mathematical proof is the way mathematicians prove unequivically that what they have proposed is correct.
Basically there are two types of proof:
Direct ProofDirect ProofA direct proof uses a sequence of logical steps to arrive at its conclusion. All steps must be based on proven facts not assumptions. Additionally we cannot use what we are trying to prove as part of the proof. There are several methods:

Indirect ProofIndirect ProofIndirect proof arrives at the conclusion by an alternate path, such as:

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