Question about ordered field axioms

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The discussion centers on the theorem regarding ordered fields, specifically addressing the relationship between inequalities. It confirms that if a > b and c ≥ d, then it follows that a + c > b + d. This conclusion is derived from the properties of ordered fields rather than being an axiom. Participants emphasize the importance of proving this theorem based on the axioms of ordered fields.

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  • Understanding of ordered fields
  • Familiarity with mathematical inequalities
  • Knowledge of axiomatic systems in mathematics
  • Basic proof techniques in mathematical logic
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  • Study the axioms of ordered fields
  • Explore theorems related to inequalities in ordered fields
  • Learn about proof techniques in abstract algebra
  • Investigate examples of ordered fields in mathematical literature
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Mathematicians, students of abstract algebra, and anyone interested in the foundational principles of ordered fields and their applications in mathematical proofs.

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If you have [itex]a > b[/itex] and [itex]c \geq d[/itex], do you have [itex]a + c > b + d[/itex]?
 
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Yes you do, but it's a theorem about ordered fields, not an axiom (usually). You may try to prove it from the axioms.
 

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