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What is the difference between a field a subfield

by student34
Tags: difference, field, subfield
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student34
#1
Nov24-13, 08:01 PM
P: 263
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.
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lurflurf
#2
Nov24-13, 08:48 PM
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.
student34
#3
Nov24-13, 09:09 PM
P: 263
Quote Quote by lurflurf View Post
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.

Number Nine
#4
Nov24-13, 09:25 PM
P: 772
What is the difference between a field a subfield

Quote Quote by student34 View Post
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?
student34
#5
Nov24-13, 10:25 PM
P: 263
Quote Quote by Number Nine View Post
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?
lurflurf
#6
Nov25-13, 01:33 AM
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.
student34
#7
Nov25-13, 04:42 AM
P: 263
Thank-you everyone!


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