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Mathematical Proof (Mathematical reasoning is important to: (Determine…
Mathematical Proof
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Terminology
In the conditional statement p -> q, p is called the hypothesis and q is called the conclusion.
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Inductive Proof
Step 1: first prove the theorem is true for when n = 1. This case is called the basis of the induction.
Step 2: we suppose the theorem is true for some value k. This assumption is called the inductive hypothesis.
Step 3: We prove that it must be true for the next value k +1. This step is called the inductive step.
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Mathematical Proof
Deductive
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Example: "Brighton is a port or a holiday resort. Brighton is not a port. Therefore, Brighton is a holiday resort"
Inductive
If a statement P(n) holds for a specific value of n, then it must hold for all n.
Example: "Most learners who did not do the tutorial questions will fail the exam. John did not do the tutorial questions. Therefore John will fail the exam".
