Incommensurable/Examples/Root 2 and 1

Example of Incommensurability

$\sqrt 2$ and $1$ are incommensurable.

Proof

From Square Root of 2 is Irrational, the ratio $\sqrt 2$ to $1$ is irrational.

Hence the result by definition of incommensurable.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): commensurable
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): commensurable