In the case of induction for example (where the base case is considered trivial): if an agent was aware of a start state (inductive hypothesis), a goal state (conclusion), and its types of operations (expression manipulations), it’s possible the agent could determine the necessary operations to create a logical path between the start state and goal state.For the “prove by induction sum(n,k=1..n)=n^2″ claim, it gave the “not always true” result because the program incorrectly failed in the base case.
At this point the application was fairly limited in terms of the number of proofs it could handle, but it performed well as a prototype or proof of concept.
When doing so, it would have searched for a possible counter-example in an attempt to disprove the claim. First, if we have Sum[s[k], {k, n}] == S[n], then the task is to verify S[n+1]-S[n] == s[n+1]. Congratulations on the project and the job. If this had correctly been interpreted as an equality, then the generated proof would verify the claim.One final, cool feature is that an invalid summation/product equality proof will be corrected with a new recommended expression:As for expression inequalities, all the generated proofs are pattern matched since I am unaware of any general-case algorithm to apply toward expression inequality proofs. steps) in order to obtain a final result. P (k) → P (k + 1). Not only is this beneficial for inequality manipulation but this is also a crucial step in case any terms need to be eliminated. At the same time, they would not likely be relying on a recipe for Gordon Ramsay’s Beef Wellington to be included in the book. The next step in mathematical induction is to go to the next element after k and show that to be true, too:. It assumed a base case of a=1, but it couldn’t properly evaluate for n. I will look further into this.is obviously false if (a-b) = 0, but there doesn’t seem to be a way to express this additional constraint.Neat post – I’m impressed that Wolfram|Alpha can generate proofs, even if it’s as restricted as this.
playing a role in generating proofs. It’s a nice idea to try to automate induction proofs, but there are some pitfalls. If the exponent r is even, then the inequality is valid for all real numbers x. For example it will not prove the statementThe helpful person at the other end answered my questions quickly, and then the conversation took a direction I didn’t expect. It didn’t make sense to reinvent the wheel, and this was when I first discovered Wolfram|Alpha’s APIs. This is a nice feature, since it ensures complete coverage of induction proofs for this query type, so long as Wolfram|Alpha doesn’t time out due to large input.Is this part of wolfram alpha? equal to 0 or 1), such as the constants, coefficients, and exponents.I am not at all suggesting that the above example would be a fun alteration to Clue; in fact, it would likely kill the fun of the game (bad joke).
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