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jhonyy9

  • 5 years ago

- is this prove correct with math induction ? -let a,b and n natural numbers from N, a>=1,b>=1,n>=3 - n=a+b+1 - how may be prove it that always for any value of n will be one a and one b that this equation is true ? - Assume there exists a natural number k such that k >= 3 and there exists a pair of natural numbers, a_k and b_k, such that (a_k + b_k + 1) = k. Let a_(k+1) = a_k. So, a_(k+1) is a natural number. Let b_(k+1) = (b_k) + 1. So, b_(k+1) is a natural number. (a_(k+1) + b_(k+1) + 1) = [a_k + ((b_k) + 1) + 1] = [(a_k + b_k + 1) + 1] = (k + 1). And (k + 1) is a natural number >= 3. So,

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  1. watchmath
    • 5 years ago
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    No need induction. Just choose \(a=n-2\) and \(b=1\)

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