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Are all types of mathematical arguments based on the following types of proofs?

Types of proofs

1. Direct proof, P -> Q

2. Proof by contradiction, [tex] \neg Q -> \neg P [/tex]

3. ~Ad absodium, P and [tex]\neg Q[/tex] -> false statement (such as 0 = 1)

I know the following types of arguments

1. Mathematical induction

2. Iterative argument

3. Least Criminals

3. The attempt at a solution

Mathematical induction seems to be a direct proof, similarly as the iterative

argument. In contrast, least criminal is apparently a combination of direct

proof, and the proof by contradiction, since least criminal argument is a

variant of Mathematical Induction.

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# Differet Types of Mathematical Arguments and Proofs

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