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There are 3 main types of mathematical proofs. These are direct proofs, proofs by contrapositive and contradiction, and proofs by induction.
Lesson Summary A flow proof is one of the ways that a proof can be formatted. The other two are a paragraph proof (in which the statements and reasons are written as sentences) and a two-column proof (in which the statements are written in one column and the reasons are written next to them in a second column).
Direct Proof: Assume p, and then use the rules of inference, axioms, defi- nitions, and logical equivalences to prove q. Indirect Proof or Proof by Contradiction: Assume p and q and derive a contradiction r r. Proof by Contrapositive: (Special case of Proof by Contradiction.)
Once a bond is issued, it offers fixed interest payments to its owner over its term to maturity, which does not change. However, interest rates in financial markets change all the time and, as a result, new bonds that are issued will offer different interest payments to investors than existing bonds.
There are many different ways to go about proving something, well discuss 3 methods: direct proof, proof by contradiction, proof by induction. Well talk about what each of these proofs are, when and how theyre used. Before diving in, well need to explain some terminology.
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One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.

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