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R → ∞ is usually read R を限りなく大きくする[と・とき] R が限りなく大きくなる[と・とき] I don't think that 「R → ∞ のとき」 is supposed to have a fixed natural pronunciation. You can ignore the の and read it as above, or you could probably read it as [R]{アール} [→]{トゥ} [∞]{インフィニティ} のとき [R]{アール} [→]{ツー} [∞]{インフィニティ} のとき


They are not grammatical phrases. We just read the symbols verbatim like: [⁠1]{いち} [+]{たす} [⁠2]{に} [=]{は} [⁠3]{さん} It has nothing different than saying: [⁠1]{いち} [+]{プラス} [⁠2]{に} [=]{イコール} [⁠3]{さん} which is also commonly heard. Though we have both [+]{たす/プラス} and [−]{ひく/マイナス}, [×]{かける} and [÷]{わる} only ...


Two common ways of translating "if and only if" use the terms 必要十分条件 ("necessary and sufficient condition") and 同値 ("equivalence"). a > b は式 (15) である為の必要十分条件である。 Equation (15) holds if and only if a > b. 式 (15) と「a>b」とは同値である。 Equation (15) is equivalent to a > b.


In the context of mathematics, 「高々 (or たかだか) 一個」 is the standard expression. 高々 can also be used in non-technical context, but it's somewhat formal. In daily conversations, we'd say "多くて(も)一個" or "最大で一個", etc.


In Japanese, R is pronounced aaru (アール) → is pronounced yajirusi (矢印【やじるし】) ∞ is pronounced mugendai (無限大【むげんだい】) I think "n→∞" is often pronounced as follows in the differential and integral. エヌ矢印無限大 enu yajirusi mugendai エヌ無限大 enu mugendai where enu (エヌ) means the letter N. Therefore I guess that "R→∞" is pronounced in the same way. Although, ...


if and only if (= iff) a > b の時、(そして/かつ)その時に限り等式が成立する。 The equation is satisfied if and only if a > b. only ... if ~なければ~ない (colloquially ~なきゃ~ない or ~なけりゃ~ない) ≈ ~ないなら~ない アイスを買ってくれなきゃ行かない。 I'll only go if you buy me an ice. ~ないと~ない この植物は定期的に水をやらないと育たない。 The plant will only grow if it is watered regularly. The difference between ...

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