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Hello,
I have a question about inductive reasoning...
Earlier this week my intro proofs class went over the logical structure of induction, and an example.
The example was a proof of [itex]\Sigma[/itex]i = n*(n + 1)/2
My main issue is the assumption that "p(k)" is true. What if it's not? I asked this in class, and my professor said it didnt matter because we are proving an implication (this made perfect sense). However, this leads to the next issue...how do you know that you're proving an implication? How can you tell when you're dealing with an implication and when not? What's the implication for this example...?
edit: it's not that I don't understand how to use it, I do. I just wrote two assigned proofs using induction. I just want to understand why it works and when it works =|
I have a question about inductive reasoning...
Earlier this week my intro proofs class went over the logical structure of induction, and an example.
The example was a proof of [itex]\Sigma[/itex]i = n*(n + 1)/2
My main issue is the assumption that "p(k)" is true. What if it's not? I asked this in class, and my professor said it didnt matter because we are proving an implication (this made perfect sense). However, this leads to the next issue...how do you know that you're proving an implication? How can you tell when you're dealing with an implication and when not? What's the implication for this example...?
edit: it's not that I don't understand how to use it, I do. I just wrote two assigned proofs using induction. I just want to understand why it works and when it works =|
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