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# Induction watch

1. Does proof by induction ONLY work for natural numbers? Is it possible to prove by induction for any n>=2 obviously depending on what is proven?

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2. You'd have to give specifics for a definitive answer, but the classic "proof by induction" concept is fairly tied to natural numbers (or at least countable variants thereof).

On the other hand, there are some proofs in real analysis etc. which have quite a flavour of "proof by induction" even if they're not directly equivalent.
3. (Original post by DFranklin)
You'd have to give specifics for a definitive answer, but the classic "proof by induction" concept is fairly tied to natural numbers (or at least countable variants thereof).

On the other hand, there are some proofs in real analysis etc. which have quite a flavour of "proof by induction" even if they're not directly equivalent.
Part c and d. To be honest that sentence doesn't even make sense to me. Anyways it doesn't mention anything about integers. I was told induction was always for natural numbers. I was thinking it might just be a typo.

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4. (Original post by cooldudeman)
Part c and d. To be honest that sentence doesn't even make sense to me. Anyways it doesn't mention anything about integers. I was told induction was always for natural numbers. I was thinking it might just be a typo.

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n is being used here to index the terms (i.e. count them: alpha1, alpha2 etc), so yes it is a natural number.
5. (Original post by davros)
n is being used here to index the terms (i.e. count them: alpha1, alpha2 etc), so yes it is a natural number.
Oh ok... really not clear though
6. Read the statements in this form:

For all natural numbers n, the conjugate of the sum of n complex numbers is the sum of their conjugates.

Then it's pretty obvious that it's actually a statement about naturals, not complex numbers.

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Updated: January 23, 2014
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