Prove that there is a natural number M such that for every natural number n, 1/n

Question

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?

anonymous · Answer

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

anonymous · Answer

right. So what I know is that $$n \ge 1$$. So couldn't we choose M= 1/M?

anonymous · Answer

M=1/n only if n and M equal 1.

anonymous · Answer

how do you know what to let M be?

anonymous · Answer

um... arbitrarily... assign a random number to M and n...

anonymous · Answer

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

anonymous · Answer

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 · Answer

...there is a natural number M... so there IS a natural number M.

anonymous · Answer

right...but Why would it let it be 1/n?

anonymous · Answer

1/n, so any 1/n would be smaller than any M... rather confused here...

anonymous · Answer

i think its just the problem... 1/n just doesn't have any special meaning here...