nLab decimal interval coalgebra

Contents

Contents

Definition

A decimal interval coalgebra is a set II with a linear order <\lt, elements 0I0 \in I, 1I1 \in I, and a partial function from \mathbb{N} to the set of endofunctions in II, III \to I

z:{m|(m<10)}(II)z:\{m \in \mathbb{N} \vert (m \lt 10)\} \to (I \to I)

such that

  • for all elements aIa \in I, 0<a0 \lt a or a<1a \lt 1

  • for all natural numbers mm \in \mathbb{N}, if m<10m \lt 10, then z(m)(0)=0z(m)(0) = 0

  • for all natural numbers mm \in \mathbb{N}, if m<10m \lt 10, then z(m)(1)=1z(m)(1) = 1

  • for all natural numbers mm \in \mathbb{N}, if m+1<10m + 1 \lt 10, then for all elements aIa \in I, it is not true that both 0<z(m+1)(a)0 \lt z(m+1)(a) and z(m)(a)<1z(m)(a) \lt 1

Examples

See also

Last revised on May 4, 2022 at 09:51:28. See the history of this page for a list of all contributions to it.