Hi! I haven't had allot of exposure to writing proofs, and am a little lost.
I am to prove that the greatest lower bound of the natural numbers is zero. I think the archimidian property might have something to do with the proof. That is, for every real number x, there exists a natural number n such that n>x.
So for the statement:
inf{ 1/n such that n is a natural number} = 0
It is possible to pick a sufficiently large real number x, such that 1/n is essentially zero, via a sort of limiting process (although limits haven't been introduced in this proof class, so I can't use them).
How would I convey this in a "rigorous" proof?
I am to prove that the greatest lower bound of the natural numbers is zero. I think the archimidian property might have something to do with the proof. That is, for every real number x, there exists a natural number n such that n>x.
So for the statement:
inf{ 1/n such that n is a natural number} = 0
It is possible to pick a sufficiently large real number x, such that 1/n is essentially zero, via a sort of limiting process (although limits haven't been introduced in this proof class, so I can't use them).
How would I convey this in a "rigorous" proof?