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# Union of two fields is a field ? watch

1. Hi everyone,
it's all in the title.
Is it true that the union of two fields is a fields ?

Thanks !!!
HIT-HEUK
2. How would you define the union of two fields? It's easy to find the union of two sets, but what about the addition and multiplication of each field?
3. (Original post by Dragon)
How would you define the union of two fields? It's easy to find the union of two sets, but what about the addition and multiplication of each field?
Oh forgot to say, they are both contained in a bigger field so there wouldn't (I guess) a problem with defining the addition and the multiplication, since it's the same for both.
4. Anyone ?
5. In general, the union of two fields is not a field.

(Now find a counterexample that shows this).
6. (Original post by DFranklin)
In general, the union of two fields is not a field.

(Now find a counterexample that shows this).
Q(sqrt(2)) U Q(sart(3)) cause sqrt(6) is not in there ...

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