The original poster is examining the properties of the field \(\mathbb{F}_2\), specifically questioning its classification as a field and the implications of its operations. The discussion revolves around the definitions and axioms that characterize fields, particularly focusing on the unique properties of the set \{0, 1\}.
The discussion is ongoing, with participants providing insights into the definitions and properties of fields. Some guidance has been offered regarding the verification of axioms, but there is no explicit consensus on the interpretations or methods to apply.
Participants are navigating through potentially confusing definitions and properties, with some expressing uncertainty about the axioms and their application to the field \(\mathbb{F}_2\). There is a noted lack of clarity regarding the operations defined for this field and how they differ from standard arithmetic.
micromass said:M3 does not state the same thing as M4...