Homotopy Type Theory Dedekind real numbers > history (Rev #10)


The locally 𝒰\mathcal{U}-small Dedekind real numbers for a universe 𝒰\mathcal{U} is defined as the Archimedean ordered integral domain 𝒰\mathbb{R}_\mathcal{U} with a strictly monotonic function i:𝕀 𝒰 𝒰i:\mathbb{I}_\mathcal{U} \to \mathbb{R}_\mathcal{U} from the locally 𝒰\mathcal{U}-small Dedekind real unit interval 𝕀 𝒰\mathbb{I}_\mathcal{U} to 𝒰\mathbb{R}_\mathcal{U} such that i(0)=0i(0) = 0 and i(1)=1i(1) = 1.

See also

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