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Learning Proof by Mathematical Induction
"... Abstract: This qualitative study of six preservice teachers ’ perceptions and performance around proof by mathematical induction indicates strengths and challenges for collegiate teaching and learning. We report on constant comparative analysis of student mathematical work and on two focus group in ..."
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Abstract: This qualitative study of six preservice teachers ’ perceptions and performance around proof by mathematical induction indicates strengths and challenges for collegiate teaching and learning. We report on constant comparative analysis of student mathematical work and on two focus group
Mathematical Induction Made Calculational
, 1994
"... Several concise formulations of mathematical induction are presented and proven equivalent. The formulations are expressed in variablefree relation algebra and thus are in terms of relations only, without mentioning the related objects. It is shown that the induction principle in this form lends ..."
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Cited by 3 (1 self)
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Several concise formulations of mathematical induction are presented and proven equivalent. The formulations are expressed in variablefree relation algebra and thus are in terms of relations only, without mentioning the related objects. It is shown that the induction principle in this form
Mathematical induction in Otterlambda
 J. Auto. Reas
"... Otterlambda is Otter modified by adding code to implement an algorithm for lambda unification. Otter is a resolutionbased, clauselanguage firstorder prover that accumulates deduced clauses and uses strategies to control the deduction and retention of clauses. This is the first time that such a f ..."
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Cited by 6 (1 self)
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of equality) and also the power of lambda unification. We illustrate how these capabilities work well together by using Otterlambda to find proofs by mathematical induction. Lambda unification instantiates the induction schema to find a useful instance of induction, and then Otter’s firstorder reasoning can
Automated Mathematical Induction
, 1992
"... Proofs by induction are important in many computer science and artiøcial intelligence applications, in particular, in program veriøcation and speciøcation systems. We present a new method to prove (and disprove) automatically inductive properties. Given a set of axioms, a wellsuited induction schem ..."
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Cited by 27 (6 self)
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Proofs by induction are important in many computer science and artiøcial intelligence applications, in particular, in program veriøcation and speciøcation systems. We present a new method to prove (and disprove) automatically inductive properties. Given a set of axioms, a wellsuited induction
Press. Mathematical Induction and Induction in Mathematics
"... However much we many disparage deduction, it cannot be denied that the laws established by induction are not enough. Frege (1884/1974, p. 23) At the yearly proseminar for firstyear graduate students at Northwestern, we presented some evidence that reasoning draws on separate cognitive systems for a ..."
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However much we many disparage deduction, it cannot be denied that the laws established by induction are not enough. Frege (1884/1974, p. 23) At the yearly proseminar for firstyear graduate students at Northwestern, we presented some evidence that reasoning draws on separate cognitive systems
Principle of Mathematical Induction for sets
"... Let S be a subset of the positive integers. Suppose that: (i) 1 ∈ S, and (ii) ∀ n ∈ Z +, n ∈ S = ⇒ n + 1 ∈ S. ..."
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Let S be a subset of the positive integers. Suppose that: (i) 1 ∈ S, and (ii) ∀ n ∈ Z +, n ∈ S = ⇒ n + 1 ∈ S.
Results 1  10
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263,536