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A field equipped with an order making it an ordered ring.
wp-ordered-fieldnlab-ordered-fieldgierz-orderEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the order to make the field an ordered ring.
Feed several structures into a construction junction and impose compatibility between them.
wp-ordered-fieldgierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Forgetting how elements were constructed leaves the usual ordered-field structure.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-rational-numbernlab-rational-numberThis is an authored directed relation from the source endpoint to the target endpoint.
Forgetting completeness and the distinguished real realization leaves an ordered field.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
nlab-real-numberEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the ordered field to have no proper algebraic ordered extension.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-real-closednlab-real-closedmilne-algebraic-number-theory