irrational number

[/ɪˈræʃənəl ˈnʌmbər/]
nounpl: irrational numbers
número irracional
1. A real number that cannot be expressed as a ratio of two integers; a number whose decimal representation is non-terminating and non-repeating
Pi (π) and the square root of 2 are examples of irrational numbers.
Pi (π) e a raiz quadrada de 2 são exemplos de números irracionais.
2. In mathematics, any real number that is not rational, meaning it cannot be written in the form p/q where p and q are integers and q ≠ 0
The set of irrational numbers is uncountably infinite.
O conjunto dos números irracionais é infinito incontável.
This is primarily a mathematical and academic term used consistently across English-speaking countries and Brazil in educational contexts. There are no significant cultural variations in usage. The concept is fundamental to mathematics education at secondary and tertiary levels in both the USA and Brazil.
Synonyms / Sinônimos
non-rational numbertranscendental number (in some cases)
Antonyms / Antônimos
rational numberintegerfraction

Regional Variations

General Brazilian Portuguese
número irracional
Standard term used in mathematics education and textbooks throughout Brazil
São Paulo
número irracional
Same as general Brazilian Portuguese; no regional variation
Portugal
número irracional
Same terminology used in European Portuguese mathematical contexts

Related Words

rational numberreal numberintegerdecimal expansionalgebraic numbertranscendental number

Related Idioms & Phrases

the irrationality of a number
irrational numbers include transcendental numbers
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