Example. $\mathbb{C}, \mathbb{Q}$ and $F(t)$ [1402]
Example. $\mathbb{C}, \mathbb{Q}$ and $F(t)$ [1402]
- $\sqrt{ 2 }, \sqrt[3]{ 2 }, i \in \mathbb{C}$ are algebraic over $\mathbb{Q}$.
- $e, \pi \in \mathbb{C}$ are transcendental over $\mathbb{Q}$. (nontrivial to prove)
- Let $F$ be a field. $t \in F(t)$ is transcendental over $F$.