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Download your document to the uploading pane on the top of the page
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Push “Done" button to the top right corner
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What is an ordered field in math?
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
Is C an ordered field?
C is not an ordered field. Proof.
What is a field in real analysis?
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
Can the complex numbers be ordered?
TL;DR: The complex numbers are not an ordered field; there is no ordering of the complex numbers that is compatible with addition and multiplication. If a structure is a field and has an ordering, two additional axioms need to hold for it to be an ordered field.
Is Q an ordered field?
Every subfield of an ordered field is an ordered field with the same ordering as the original one. Since QR, it is an ordered field. The same holds true, for example, for the field Q[2]R as well.
What is an example of a field?
The set of real numbers and the set of complex numbers each with their corresponding + and * operations are examples of fields. However, some non-examples of a field include the set of integers, polynomial rings, and matrix rings.
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