# Using the Archimedean principle

How can I use the Archimedean principle to show that there exists an integer $$n$$ such that $$\frac{1}{n} where $$x$$ and $$y$$ are real numbers with $$0\leq x?

According to the Archimedean principle: Let $$a>0$$ and $$b \in \mathbb{R}$$. There exists an integer $$n \in \mathbb{N}$$ such that $$b.

• How you express the Archimedean principle ? – Mauro ALLEGRANZA Feb 5 at 15:26
• @MauroALLEGRANZA I added the description in the question now. – Jake Feb 5 at 15:28

You apply the definition. Because $$x \lt y, y-x \gt 0$$. Let $$y-x$$ be the $$a$$ in the definition and $$b$$ be $$1$$.