Whenever an arbitrary positive quantity 𝞮 is assigned,we can make off an interval |x - x0| < 𝞭 so small that for any x which belongs both to the domain of f and to that interval the inequality |f(x) - η| < 𝞮 holds. (查看原文)
if f(𝞷) is defined, then lim(x -> 𝞷) f(x), if it exists at all, must have the value f(𝞷). Indeed, the definition of η = lim(x -> 𝞷)f(x) implies in particular | f(𝞷) - η |<𝞮 for every positive 𝞮 and hence f(𝞷) = η (查看原文)
The word 'rational' here does not mean reasonable or logical but is derived from the word 'ratio' meaning the relative proportion of two magnitudes. (查看原文)
