# Homotopy Type Theory strongly extensional function > history (Rev #1, changes)

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# Contents

## Definition

Given a sequentially Cauchy complete Archimedean ordered field $\mathbb{R}$, a function $f:\mathbb{R} \to \mathbb{R}$ is strongly extensional if for every $x:\mathbb{R}$ and $y:\mathbb{R}$, $\vert f(x) - f(y) \vert \gt 0$ implies that $\vert x - y \vert \gt 0$.

In particular, this definition applies to Dedekind real numbers, which is used for proving Brouwer's theorem? in real-cohesive homotopy type theory.