Commensurability is Transitive
Let $a$, $b$, $c$ be three real numbers.
Then $a$ and $c$ are commensurable.
From the definition of commensurablility:
- $\dfrac a b, \dfrac b c \in \Q$
- $\dfrac a b \times \dfrac b c \in \Q$
Cancelling $b$, we have:
- $\dfrac a c \in \Q$
Hence the result.