Proof let 1) nt 1 Base case: P1-1/2 Inductive step: suppose Pn) has already been

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Proof let 1) nt 1 Base case: P1-1/2 Inductive step: suppose Pn) has already been proven for some arbitrary n. The statement Pin+1) is k(K This concludes the proof by induction. n +2 The proof abuses the notation Pin) to refer to both the common value of the two sides of the equation to be proved and the stotement that the two sides are indeed equal as the notation was introduced in the lecture. Furthermore, it does not make sense to define Pin) as the common value of the two sides, because it assumes the conclusion, that the two sides are equal. At the very least, the definition of PIn) in the first line should have used parentheses: n+ 1 Related to that. PI1) is not the quantity 1/2. It's the statement (1/2 1/2). The best option 1s to not use the abstraction of P n in actual inductive proofs at all but refer verbally to the statement to be proved The notation P njis best reserved for discussing the logic of inductive proofs in the abstract The proof writer confused stoting Pn+1 with showing that it must be true, given Pin) is true. There is nothing wrong with this proof. The statement Pin 1) s glven incoectly. The correct one is Pin+1)= n+2

Explanation / Answer

its option 2,

the proof writer confused stating p(n+1) with out showing it is true

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