noun
definition
An incommensurable value or quantity; an irrational number.
adjective
definition
Of two real numbers, such that their ratio is not a fraction of two integers.
definition
(arithmetics) Of two integers, having no common integer divisor except 1.
definition
Not able to be measured by the same standards as another term in the context.
example
The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.
Examples of incommensurable in a Sentence
A non-terminating simple continued fraction must be incommensurable.
For us with the standard of good and evil given us by Christ, no human actions are incommensurable.
Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.
But for the literary life of both poets the gain was incommensurable.
Arithmetic, algebra, and the infinitesimal calculus, are sciences directly concerned with integral numbers, rational (or fractional) numbers, and real numbers generally, which include incommensurable numbers.
Furthermore, incommensurable numbers are defined as the limits arrived at as the result of certain procedures with rational numbers.
In an antilogarithmic table, the logarithms are exact quantities such as 00001, 00002, &c., and the numbers are incommensurable.
If the number is incommensurable or consists of more than seven figures, we can take the first seven figures of it (or multiply and divide the result by any factor, and take the first seven figures of the result) and proceed as before.
This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.
His incommensurable and indescribable masterpiece of mingled humour, wisdom, satire, erudition, indecency, profundity, levity, imagination, realism, reflects the whole age in its mirror of hyperAristophanic farce.
Any quantity, commensurable or incommensurable, can be expressed uniquely as a simple continued fraction, terminating in the case of a commensurable quantity, non-terminating in the case of an incommensurable quantity.
In the introduction to his work Von der Weltseele, however, he argues in favour of the possibility of a transmutation of species in periods incommensurable with ours.
If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- - n n -3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."
These results were given by Lambert, and used by him to !prove that r and ir 2 are incommensurable, and also any commensurable power of e.
But an investigation of dependent lines which are often incommensurable forces us to adopt the contradictory fiction of partially overlapping, i.e.