Recent content by FallMonkey

The problem is I don't know what fied isomorphism is (maybe for the whole semester) and when I asked professor if I needed to know about field isomorphism to solve this question he anwsered no. Only thing I know and related to isomorphism is Peano isomorphism I learned in number system. I...

Ouch, so the uniqueness I'm trying to find is actually not there? Ahh the theorem of real closed field with unique ordering must be understood terribly be me. I think for one day I totally complicated the problem too far, while at first guess that P1,P2,+Z,-Z(which I can't prove to be wrong...

Are you still there, Dick...m(-_-)m

Oh good morning, wish you a nice dream. yes I do have no way of telling the difference between the two using field operations, just like that I can't tell the difference between P1 with Z in it and P2 with -Z in it. Is that breaking the uniqueness? I thought I could find a contradiction and...

Ehh sorry my bad understanding and stupidity. So for Q[sqrt(2)], either sqrt(2) is in P or -sqrt(2) is in P. And we know all a+bsqrt(2) will be in Q. by constructing two field ordering of Q[sqrt(2)], and by proving that sqrt(2) is always in P, we have the contradiction, therefore the...

By applying taylor series to express sqrt(2) as result of a series of rational numbers I guess? Therefore any irrational number must be in P...and then we could get to real number field. But it's still not a general field, and I can't prove the uniqueness of its order. It's a real...

Ahh, my stupidity. I mistook {1,0} for (0,1). Sorry and thanks for your kindness. Now everything explains.

Homework Statement Is the ordering of a ordered field unique? That is, is it possible to have different ordering set(the order), we call P1 and P2, both able to make a field F into a ordered field? Homework Equations no. The Attempt at a Solution First I tried to assume now...

Now that Fs is function from [0,1] to {0,1}, then how could f(x)=1 if 1 is not in the codomain? And what do you mean by " functions in A that can be defined as stated in the start of this proof", if we only define it from [0,1] to {0,1}? Am I missing something? Though this is a classic proof...

That's such amazing rephrase, I suddenly feel I have more for it. Thanks for the tips, I'll see what I can do now.

Homework Statement Is it possible to construct a field, that satisfies all basic propeties (http://en.wikipedia.org/wiki/Field_%28mathematics%29#Definition_and_illustration , the six bolded part ), with only and all positive integers? Remeber, you don't have 0/negative numbers/fraction in...