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## Homework Statement

Use the Archimedean property of [itex] \mathbb{R} [/itex] to prove that

the greatest lower bound of [itex] {\frac{1}{n}:n\in\mathbb{N}}=0 [/itex]

the archimedean principle says that for any number y there is a natural number

such that 1/n<y for y>0

## The Attempt at a Solution

since all of our numbers in our set are positive. I could pick a real number as close to zero as I wanted but there would still be a natural such that 1/n is smaller than the real I picked, there zero is the greatest lower bound of the set.