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Results tagged with fields
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user 483446
Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].
4
votes
Eudoxus real numbers
The rational numbers are an ordered subfield of every ordered field, and are initial in the category of ordered fields, and so they can be characterised as the initial ordered subfield of the Eudoxus real …
- 2,624
5
votes
3
answers
546
views
The field structure on the locale of real numbers
It is well known how to derive the field operations from the construction of the real numbers as the Dedekind completion of the rational numbers and as the Cauchy completion of the rational numbers; s …
- 2,624
0
votes
Sequential colimit of iterated quotients of Cauchy sequences
$\mathrm{QuotCauchy}$ defined above is an endofunctor on the category of Archimedean ordered fields. …
- 2,624
8
votes
1
answer
231
views
Sequential colimit of iterated quotients of Cauchy sequences
If $F$ is already Cauchy complete, then the field homomorphism is a field isomorphism, but this usually cannot be proven for arbitrary Archimedean ordered fields $F$ in constructive mathematics. … implies that one could repeatedly construct the quotient set of Cauchy sequences starting from the rational numbers, yielding a sequence of unique injective field homomorphisms between Archimedean ordered fields …
- 2,624