anonymous
  • anonymous
Prove that there is a natural number M such that for every natural number n, 1/n
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
ill try my best: because a fraction is always smaller than a whole number, 1/n is always smaller than M.
anonymous
  • anonymous
right. So what I know is that \[n \ge 1\]. So couldn't we choose M= 1/M?
anonymous
  • anonymous
M=1/n only if n and M equal 1.

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anonymous
  • anonymous
how do you know what to let M be?
anonymous
  • anonymous
um... arbitrarily... assign a random number to M and n...
anonymous
  • anonymous
because if M = 5, for example, then 1/n will always be smaller, n being a random integer.
anonymous
  • anonymous
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
anonymous
  • anonymous
...there is a natural number M... so there IS a natural number M.
anonymous
  • anonymous
right...but Why would it let it be 1/n?
anonymous
  • anonymous
1/n, so any 1/n would be smaller than any M... rather confused here...
anonymous
  • anonymous
i think its just the problem... 1/n just doesn't have any special meaning here...

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