Proofs that 0.999... = 1 which directly use these constructions are not found in textbooks on real analysis, where the modern trend for the last few decades has been to use an axiomatic analysis.
直接用到这些结构的0.999… = 1的证明，现在已经无法在實分析的教科书中找到了；最近几个年代的趋势，是使用公理化的分析。