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anonymous

  • 5 years ago

Prove that there is a natural number M such that for every natural number n, 1/n <m. I have an idea but am not sure its right?

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  1. anonymous
    • 5 years ago
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    ill try my best: because a fraction is always smaller than a whole number, 1/n is always smaller than M.

  2. anonymous
    • 5 years ago
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    right. So what I know is that \[n \ge 1\]. So couldn't we choose M= 1/M?

  3. anonymous
    • 5 years ago
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    M=1/n only if n and M equal 1.

  4. anonymous
    • 5 years ago
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    how do you know what to let M be?

  5. anonymous
    • 5 years ago
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    um... arbitrarily... assign a random number to M and n...

  6. anonymous
    • 5 years ago
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    because if M = 5, for example, then 1/n will always be smaller, n being a random integer.

  7. anonymous
    • 5 years ago
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    right but that is because n was a whole number but when its 1/n, that makes it smaller that M. I am just confused on how you would know what to let M be? I have an exam coming up and I am trying to practice, but these proofs that deal with inequalities are killing me

  8. anonymous
    • 5 years ago
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    ...there is a natural number M... so there IS a natural number M.

  9. anonymous
    • 5 years ago
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    right...but Why would it let it be 1/n?

  10. anonymous
    • 5 years ago
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    1/n, so any 1/n would be smaller than any M... rather confused here...

  11. anonymous
    • 5 years ago
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    i think its just the problem... 1/n just doesn't have any special meaning here...

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