lurflurf said:That should say something like
"A subfield of a field is any subset of the field that is itself a field (with the same operations)."
What you have
"Any subfield (together with the addition and multiplication) is again a field".
Is true, but not very useful without context.
student34 said:I still don't understand why Q is a subfield of R, but Z isn't.
Number Nine said:Is Z a field?
What are the field axioms?
A field refers to a broad area of study, such as biology or physics, that encompasses multiple subfields. A subfield, on the other hand, is a more specific area of research within a larger field. For example, within the field of biology, there are subfields such as genetics, ecology, and microbiology.
Yes, all subfields are part of a larger field. They are more specialized areas of study that contribute to the overall understanding of a particular field.
Yes, a subfield can belong to multiple fields. For instance, the subfield of biochemistry can be considered part of both biology and chemistry.
Fields and subfields are determined based on the subject matter and the focus of research within a particular area. They are often defined by the scientific community and can evolve over time as new discoveries are made.
While fields and subfields may have some overlap in methodologies, they often have distinct approaches and techniques that are specific to their focus of study. This allows for a more thorough understanding of the subject matter and allows for collaboration between different fields and subfields.