ɪn mˌæθɪmˈæɾɪks, ɐ pˈɛɹən nˈʌmbɚɹ ɪz ɐn ˌældʒɪbɹˈeɪɪk ˈɪntɪdʒɚɹ ˈælfə wˌɪtʃ ɪz ɹˈiːəl ænd ɛksˈiːdz wˈʌn, bˌʌt sˈʌtʃ ðæt ɪts kˈɑːndʒuːɡˌeɪt ˈɛlɪmənts ɑːɹ ˈɔːl lˈɛs ðɐn ˈælfə ɪn ˈæbsəlˌuːt vˈæljuː.
In mathematics, a Perron number is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than α in absolute value.