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What is the difference between a field a subfield 
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#1
Nov2413, 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. 


#2
Nov2413, 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. 


#3
Nov2413, 09:09 PM

P: 263




#4
Nov2413, 09:25 PM

P: 772

What is the difference between a field a subfield
What are the field axioms? 


#5
Nov2413, 10:25 PM

P: 263




#6
Nov2513, 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.



#7
Nov2513, 04:42 AM

P: 263

Thankyou everyone!



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