Definitions for irrational number
ir·ra·tional num·ber

Princeton's WordNetRate this definition:5.0 / 1 vote

1. irrational number, irrationalnoun

   a real number that cannot be expressed as a rational number

WiktionaryRate this definition:0.0 / 0 votes

1. irrational numbernoun

   Any real number that cannot be expressed as a ratio of two integers.

WikipediaRate this definition:0.0 / 0 votes

1. Irrational number

   In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational.Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat. Conversely, a decimal expansion that terminates or repeats must be a rational number. These are provable properties of rational numbers and positional number systems, and are not used as definitions in mathematics. Irrational numbers can also be expressed as non-terminating continued fractions and many other ways. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.

ChatGPTRate this definition:0.0 / 0 votes

1. irrational number

   An irrational number is any real number that cannot be expressed as a quotient or ratio of two integers (where the denominator is not zero). This means that an irrational number cannot be represented as a simple fraction and its decimal representation is non-terminating (it never ends) and non-repeating. Examples of irrational numbers include the square root of 2, the value of pi, and the natural logarithm e.

WikidataRate this definition:4.5 / 2 votes

1. Irrational number

   In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable it follows that almost all real numbers are irrational. When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common. Perhaps the best-known irrational numbers are: the ratio of a circle's circumference to its diameter π, Euler's number e, the golden ratio φ, and the square root of two √2.

Matched Categories

1. • Real Number

How to pronounce irrational number?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Karen

   Australian

   Hayley

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   Priya

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   Neerja

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Numerology

1. Chaldean Numerology

   The numerical value of irrational number in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of irrational number in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=irrational number
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Irrational_Number
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Irrational_Number
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=irrational number