- #1
CubicFlunky77
- 26
- 0
This is the first 'problem' in my Linear Algebra/Geometry textbook. 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.
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]
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]