Meanwhile, laughter is pleasantly irrational and might also have contributed to the death of Hippasus.
Being put in a place can be deduced as the ratio of one personality crossing a situation to the circumference of the whole situation, and is itself irrational ([pi]).
The Hindus recognized that quadratic equations have two roots, and included negative as well as irrational roots.
They could solve quadratic equations, recognizing two solutions, possibly irrational, but usually rejected negative solutions.
However, if x is irrational
then x = p + [pi]/k [member of] B or x [member of] C.
For the object designated by the inexpressible term of irrational ratio cannot exist, and it is possible to demonstrate that, in the universe of the ratio, its ontic status is that of absolute Non-Being.
And it was to all appearances to the recognizable character of that irrational ratio that the proposition -- as beautiful as it was mysterious -- alluded, which the great Parmenides uttered, in Plato's dialogue bearing his name, against his own thesis: `What is said to be non-being is no less cognizable than that from which it is different -- [GREEK TEXT NOT REPRODUCIBLE IN ASCII].
According to a recently developed method of assessing the randomness of a sequence of numbers, however, the digits of pi turn out to be more irregular than the digits of the other irrational numbers.
Because the approximate entropy method does not depend on any assumptions about the process involved in generating a sequence of numbers, it can be applied to biological and medical data and to physical measurements, such as the number of alpha particles emitted by a radioactive nucleus in specified time intervals, as readily as to the digits of irrational numbers.
A popular view is that the great discovery of Pythagoreans was that there are irrational
numbers, for example, the positive square root of two.
You could have negative integers, negative fractions, and negative irrationals