# Irrational

• (adj): Not consistent with or using reason.
Example: "Irrational fears"; "irrational animals"

### Some articles on irrational:

Complete Quotients and Equivalent Real Numbers - A Theorem About "equivalent" Irrational Numbers
... Amazingly enough, two irrational numbers x and y are equivalent under this scheme if and only if the infinitely long "tails" in their expansions as regular continued fractions are exactly ... Let x and y be two irrational (real) numbers, and let the kth complete quotient in the regular continued fraction expansions of x and y be denoted by ζ k and ψ k, respectively, Then x ~ y (under the equivalence ...
Irrational Number - Open Questions
... It is not known whether π + e or π − e is irrational or not ... pair of non-zero integers m and n for which it is known whether m π + n e is irrational or not ... or the Euler–Mascheroni gamma constant γ are irrational ...
Algebraic Fraction - Irrational Fractions
... An irrational fraction is one that contains the variable under a fractional exponent ... An example of an irrational fraction is The process of transforming an irrational fraction to a rational fraction is known as rationalization ... Every irrational fraction in which the radicals are monomials may be rationalized by finding the least common multiple of the indices of the roots, and ...
Proof That π Is Irrational
... The number π (pi) has been studied since ancient times, and so has the concept of irrational numbers ... An irrational number is any real number that cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer ... It was not until the 18th century that Johann Heinrich Lambert proved that π is irrational ...
Economy And Society - Quotes - Ideal Types (Pure Types)
... analysis it is convenient to treat all irrational, affectually determined elements of behavior as factors of deviation from a conceptually pure type of rational action ... what the course of action would have been if it had not be influenced by irrational affects it is then possible to introduce the irrational components as accounting for ... to understand the ways in which actual action is influenced by irrational factors of all sorts, such as affects and errors, in that they account for the deviation ...

### More definitions of "irrational":

• (adj): Real but not expressible as the quotient of two integers.
Example: "Irrational numbers"

### Famous quotes containing the word irrational:

How did reason enter the world? As is fitting, in an irrational way, accidentally. We will have to guess at it, like a riddle.
Friedrich Nietzsche (1844–1900)

The irrational may be attractive in the abstract, but not in cab drives, dinner guests, or elderly relatives.
Mason Cooley (b. 1927)

It is not to be forgotten that what we call rational grounds for our beliefs are often extremely irrational attempts to justify our instincts.
Thomas Henry Huxley (1825–95)