Existence of a Sequence of Positive Real Numbers with Limit Zero

Let $\mathbb{R}$ denote the real numbers, with the order $\le$ of the ordered field and the additive identity $0$ of the underlying field; write $x<y$ to mean $x\le y$ and $x\ne y$.

Then there exists a sequence $(h_k)_{k\in\mathbb{N}}$ in $\mathbb{R}$ such that $0<h_k$ for every $k\in\mathbb{N}$ and such that $(h_k)_{k\in\mathbb{N}}$ has limit $0$.