Infinity and infinitesimal - mugendaimugensho (English spelling) infinite(infinity), infinitesimal

Japanese: 無限大･無限小 - むげんだいむげんしょう（英語表記）infinitum(infinity)，infinitesimal

Two new elements, written as +∞ and -∞, are added to the whole set of real numbers, which are named positive infinity and negative infinity, respectively, and a magnitude relationship is established such that for all real numbers a , -∞ < a < +∞. +∞ is sometimes simply written as ∞ and called infinity. If there is a sequence of real numbers { x _n }, and as n →∞, if x _n →∞, then x _n is said to become (positive) infinity, if x _n → -∞, then x _n is said to become negative infinity, and if x _n → 0, then x _n is said to become infinitesimal. If x _n becomes positive or negative infinity, then 1/ x _n becomes infinitesimal.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

実数全体に，＋∞，－∞と書く新しい二つの要素をつけ加えて，それぞれ正の無限大，負の無限大と名付け，すべての実数aに対して－∞＜a＜＋∞なる大小関係を規約する。＋∞を単に∞と書き，無限大と呼ぶこともある。実数列｛x_n｝があって，n→∞のとき，x_n→∞となるならばx_nは(正の)無限大になるといい，x_n→－∞となるならばx_nは負の無限大になるといい，またx_n→0となるならばx_nは無限小になるという。x_nが正または負の無限大になるならば1/x_nは無限小となる。

出典　株式会社平凡社世界大百科事典第２版について　情報

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