Math 2.0

Field theory and polynomials Proposition

Archimedean property

Builds on Archimedean ordered field

Statement

Let FF be an Archimedean ordered field and let xx be an element of FF. Then there is a natural number nn with x<nx < n.

Remarks

Proof: apply the definition with y=1y = 1. Thus the natural numbers are not bounded above in FF. The real numbers are Archimedean, thus this holds for each real number xx.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Ordered field, definition, no evidence levelOrdered fielddefinitionArchimedean ordered field, definition, no evidence levelArchimedean ordered f…definitionArchimedean property, statement, no evidence levelArchimedean propertystatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Ordered field definition
  2. Archimedean ordered field definition
  3. Archimedean property statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Archimedean_property, Ordered fields
About this page
Tag0A74SX55QP
URIm2://0A74SX55QP
Kindstatement, proposition
WritingW0 stub
MSC12J15
StatusThis copy of the site has no build data. Run m2 status 0A74SX55QP.
UsesArchimedean ordered field
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