What does it mean for the real numbers to be Archimedean?
Every real number is rational
For any positive real ϵ\epsilonϵ, there exists n∈Nn \in \mathbb{N}n∈N with 1n<ϵ\frac{1}{n} < \epsilonn1<ϵ
The real number line has no gaps
Every bounded sequence converges