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How to prove an expression by method of mathematical induction?
10 years ago
I want to prove the expression by method of mathematical induction with Mathematica, but I do not know how to start. How do I tell Mathematica to do that?
S <- 0
i <- 0
while i < n
S <- S + n
i <- i + 1
Basis Step: k = 0. When k = 0, that is when the loop is not entered, S = 0 and i = 0. Hence S = k*n and i = k hold.
Induction Hypothesis: For an arbitrary value m of k, S = m * n and i = m hold after going through the loop m times.
Inductive Step: When the loop is entered (m + 1)-st time, S = m*n and i = m at the beginning of the loop. Inside the loop,
S <- m*n + n
i <- i + 1
producing S = (m + 1)*n and i = m + 1.
Thus S = k*n and i = k hold for any natural number k.
Sean Clarke, Wolfram Research
10 years ago
Are you familiar with Coq or Isabelle? Are you comparing Mathematica to those kinds of theorem-proving languages?
I apologize, but I'm not sure how to make sense of this question in light of what Mathematica is. It looks like you're trying to resolve a statement in Hoare logic which requires induction. You could probably write some functionality like this into Mathematica, but you don't really do induction proofs in the same sense with Mathematica that you would with say, Coq.
Please first familiarize yourself with the basics of Mathematica and what it does. This will help us better understand your question.
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