query: How to prove that every ordered field has a subfield isomorphic to $\mathbb{Q}$ using a certain provided function?
positive_passages.docid: 155125
positive_passages.text: Every ordered field has a subfield isomorphic to $\mathbb Q$?
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 31722
negative_passages.text: Prove $-(-a)=a$ using only ordered field axioms
negative_passages.docid: 79734
negative_passages.text: Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
negative_passages.docid: 4401
negative_passages.text: Constructive proof that algebraic numbers form a field
negative_passages.docid: 138632
negative_passages.text: Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
negative_passages.docid: 120522
negative_passages.text: Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 10111
negative_passages.text: Prove or disprove that Q[√2] is a field
negative_passages.docid: 156859
negative_passages.text: Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.
negative_passages.docid: 115129
negative_passages.text: Constructing an explicit isomorphism between finite extensions of finite fields
negative_passages.docid: 6855
negative_passages.text: Subfields of finite fields
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 39514
negative_passages.text: how do I prove that $1 > 0$ in an ordered field?
negative_passages.docid: 112909
negative_passages.text: is a number field by definition a subfield of $ \mathbb C $?
negative_passages.docid: 63280
negative_passages.text: Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.