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Mathematics, 23.06.2019 15:30 swaggernas

Find the error in the following proof that all students at penn state have the same gpa. indicate the first sentence that is incorrect. explain why it is incorrect. claim: in every set of n penn state students, all students have the same gpa. proof: by induction on n. base case: n = 1. in every set containing just one penn state student, all students clearly have the same gpa. induction step: for k ≹ 1 assume that the claim holds for n = k and prove that it holds for n = k + 1. take any set s of k + 1 penn state students. remove one student from this set to obtain the set s1 with k students. by the induction hypothesis, all students in s1 have the same gpa. now replace the removed student and remove a different one to obtain the set s2. by the same argument, all students in s2 have the same gpa. therefore, all the students in s must have the same gpa.

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Find the error in the following proof that all students at penn state have the same gpa. indicate th...
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