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Results tagged with ordered-fields
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user 483446
6
votes
1
answer
334
views
Proper definition of ordered field in constructive mathematics
The nLab article on ordered fields defines ordered fields to be a field $K$ with a strict linear order $<$ such that $0 < 1$ and for all elements $a \in K$ and $b \in K$, if $a > 0$ and $b > 0$ then $ …
- 2,624
6
votes
1
answer
278
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Archimedean ordered fields without maxima and minima in constructive mathematics
In constructive mathematics, let us define an ordered (Heyting) field $F$ to be a commutative ring with a binary relation $<$ which is
irreflexive, where for all $x$, $\neg (x < x)$
asymmetric, where …
- 2,624
6
votes
0
answers
108
views
Archimedean ordered field in which every function is smooth
In constructive mathematics, it is consistent that every function $\mathbb{R} \to \mathbb{R}$ on the Dedekind real numbers is continuous. However, it is not consistent that every function $\mathbb{R} …
- 2,624
4
votes
1
answer
258
views
Constructing ordered fields with lattice structure from ordered fields without lattice struc...
This post originated from my reference request for the definition of an ordered field in constructive mathematics: Proper definition of ordered field in constructive mathematics
We are working in cons …
- 2,624