This is the first 'problem' in my Linear Algebra/Geometry text book. I just need to know if I am doing it correctly. Any hints? I also need to know if I am using correct notation/presentation.(adsbygoogle = window.adsbygoogle || []).push({});

Question: [itex]\mathbb R^+ \leftrightarrow \mathbb Q[/itex]?

What I've done:

Suppose: [itex](ε_1,...,ε_n) \in \mathbb R^+ \rightarrow \mathbb K[/itex] and

[itex](c_1,...,c_n) \in \mathbb Q \rightarrow \mathbb K[/itex]

Assuming: [itex]\mathbb R^+ ⊂ \mathbb K[/itex] and [itex]\mathbb Q ⊂ \mathbb K[/itex] where [itex]\mathbb K[/itex] is a numerical/object field; we can say that

[itex] \forall (ε \in \mathbb R^+, c \in \mathbb Q) \in \mathbb K \exists (ε \cap c) \in (\mathbb R^+ \bigcap \mathbb Q)[/itex] |[itex]\mathbb R^+ \leftrightarrow \mathbb Q[/itex]

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# Trying to show that rationals exist on the + real number line field K

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