incommensurable

Etymology

From Middle French incommensurable, from Medieval Latin incommensurabilis. Its full etymology is equivalent to that of in- + commensurable.

adj

1. (mathematics, of two real numbers) having a ratio that is not expressible as a fraction of two integers.
   The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.
2. (mathematics, of two integers) having no common integer divisor except 1.
3. Not able to be measured by the same standards as another term in the context.

noun

1. An incommensurable value or quantity; an irrational number.
   Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy. 1946, Bertrand Russell, chapter 3, in History of Western Philosophy