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Irrational
(redirected from Irrationals)

   Also found in: Dictionary/thesaurus, Medical, Legal, Wikipedia 0.01 sec.
irrational
1. Maths
a. not rational
b. (as noun)
2. Prosody in Greek or Latin verse
a. of or relating to a metrical irregularity, usually the occurrence of a long syllable instead of a short one
b. denoting a metrical foot where such an irregularity occurs

Irrational 

in the most general meaning, that which is beyond the bounds of reason; alogical or nonintellectual; incommensurable with rational thinking or even contradicting it. The irrational is generally contrasted with the rational. The irrational as something inaccessible to rational cognition and inexpressible in logical concepts is one of the basic reference points for a number of idealistic currents, jointly referred to as philosophical irrationalism (for example, intuitionism and voluntarism). In the religious world view the rational is viewed as prerational (spontaneous-chaotic, not shaped by the Logos), as distinguished from both the rational and suprarational (the mystical, given in revelation).

In the theory of knowledge of dialectical materialism the irrational is understood to be something not yet known but knowable in principle.



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It is hard to introduce (or review) fractions, and present convincing examples of numbers that are not fractions, namely, irrationals.
Aleph-one counts all the real numbers--the rationals plus the irrationals such as pi and the square root of z.
Given the fact that the interval between 1 and the square root of 2 is less than 1/2, it might seem unfathomable that the numbers in this interval contain an uncountably infinite set of irrationals.
 
 
 
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