Two positive real numbers and are commensurable, iff there exists a positive real number such that
with some positive integers and . If the positive numbers and are not commensurable, they are incommensurable.
Conversely, if (2) is valid with , then we can write
which means that and are multiples of and thus commensurable. Q.E.D.
Example. The lengths of the side and the diagonal of http://planetmath.org/node/1086square are always incommensurable.
0.1 Commensurability as relation
|Date of creation||2013-03-22 18:11:14|
|Last modified on||2013-03-22 18:11:14|
|Last modified by||pahio (2872)|