A billion worlds; the worlds that constitute the domain of the Buddha.
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A world consists of the world of desire and the first dhyāna heaven [初禪天] of the world of form [色界] (i.e., the heaven of the Brahmā followers [梵衆天], the heaven of Brahmāʼs ministers [梵輔天], and the heaven of Mahābrahmā [大梵天]).
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One thousand times one thousand times one thousand makes one billion. Commonly abbreviated as 三千; 三千界, 三千世界. It is a way of describing the vastness and interwovenness of the universe in ancient Indian cosmology.
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(Skt. trisāhasra-mahāsāhasra-loka-dhātu, tri-sāhasra-mahā-sāhasro lokadhātuḥ, tri-sāhasra-mahā-sāhasrako lokaḥ tri-sāhasra-mahā-sāhasra; Pāli ti-sahassī-mahā-sahassīloka-dhātavo). 〔起信論 T 1666.32.583a28〕 [Charles Muller; source(s): Ui, Nakamura, Hirakawa, JEBD, Iwanami]
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Mt. Sumeru and its seven surrounding continents, eight seas and ring of iron mountains form one small world [小世界]; 1,000 of these form a small chiliocosm [小千世界]; 1,000 of these small chiliocosms form a medium chiliocosm [中千世界]; a thousand of these form...
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…a great chiliocosm [大千世界], which thus consists of 1,000,000,000 small worlds. The三千indicates the above three kinds of thousands, therefore三千大千世界is the same as 大千世界, which is one Buddha-world. Also see 一大三千世界. [Charles Muller; source(s): Soothill, Nakamura]
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)*(1000
) = 1,000,000,000