Duba wurin da ke ƙasa sannan ka amsa tambayar daga baya a cikin harshe ɗaya kamar yadda wurin yake:  Passage: A cikin wannan tsari, daidaito 1 = 0.999... da 1 = 1.000... suna nunawa, bi da bi, gaskiyar cewa 1 yana cikin duka [0, 1] da [1, 2], don haka mutum zai iya zaɓar ko dai wani yanki lokacin da yake neman lambobi. Don tabbatar da cewa wannan alamar ba ta amfani da alamar "=" ba, wanda yake buƙatar hanyar sake gina ainihin lambobi na musamman ga kowane nau'i. Ana iya yin wannan tare da iyaka, amma sauran gine-gine suna ci gaba da batun tsari. Zaɓin ɗaya mai sauƙi shine ka'idar tazara ta tsakiya, wanda ke ba da tabbacin cewa an ba da jerin tsararru, tsararru masu rufewa waɗanda tsayinsu ya zama ƙarami, tsararru suna ƙunshe da ainihin lamba ɗaya a cikin mahaɗar su. Don haka b0.b1b2b3... an ayyana shi a matsayin lamba ta musamman da ke cikin dukkan tazarar [b0, b0 + 1], [b0.b1, b0.b1 + 0.1], da sauransu. 0.999... to shi ne ainihin lambar da ta kasance a cikin dukkan tazarar [0, 1], [0.9, 1], [0.99, 1], da kuma [0.99...9, 1] ga kowane madaidaicin jerin 9s. Tun da 1 yana da wani kashi na kowane daga cikin wadannan jinkiri, 0.999... = 1.The Nested Intervals Theorem ne yawanci kafa a kan wani more muhimman hakkokin halayyar da real lambobi: da wanzuwar kalla babba iyaka ko suprema. Don amfani da waɗannan abubuwa kai tsaye, mutum na iya ayyana b0.b1b2b3... a matsayin mafi ƙarancin iyakar sama na saitin masu kusanci {b0, b0.b1, b0.b1b2,...}. Mutum zai iya nuna cewa wannan ma'anar (ko ma'anar tazara mai ma'ana) ya dace da tsarin rarrabawa, yana nuna 0.999... = 1 kuma. Tom Apostol ya kammala da cewa,  Tambaya: Mene ne halayyar lambar da aka ambata?
lambar ta musamman