# What is the difference between a field a subfield

by student34
Tags: difference, field, subfield
 P: 264 For example, my notes say, "Q (rationals) is a subﬁeld of R (reals). Z (integers) is not a subﬁeld of R. Any subﬁeld (together with the addition and multiplication) is again a ﬁeld". This just doesn't make any sense to me. Oops, this was suppose to be in the homework section - sorry.
 HW Helper P: 2,264 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.
P: 264
 Quote by lurflurf 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.
I still don't understand why Q is a subfield of R, but Z isn't.

P: 772
What is the difference between a field a subfield

 Quote by student34 I still don't understand why Q is a subfield of R, but Z isn't.
Is Z a field?
What are the field axioms?
P: 264
 Quote by Number Nine Is Z a field? What are the field axioms?
Oh, is it not a field because division of 2 integers can produce a number that isn't an integer?
 HW Helper P: 2,264 ^Yes. A subset is a subfield if it is itself a field (with the same operations). Z is not a field, so it is not a subfield.
 P: 264 Thank-you everyone!

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