Archimedean property

Statement

Let $F$ be an Archimedean ordered field and let $x$ be an element of $F$. Then there is a natural number $n$ with $x < n$.

Remarks

Proof: apply the definition with $y = 1$. Thus the natural numbers are not bounded above in $F$. The real numbers are Archimedean, thus this holds for each real number $x$.

Explanations

L1 human

No element of an Archimedean field is larger than all the natural numbers. For example, for the real number $x = 10^{6} + 0.5$, the natural number $n = 10^{6} + 1$ is larger.