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My guess would be that as each DVD is divided into a variable number of chapters, and each chapter is of a variable length, you would have to be unlucky to find two different DVDs that matched on both counts, and that's where the unique identification of recently inserted discs becomes possible.
The first thing a DVD player does when it fires up is to check those numbers, and if it 'recognises' the disc inserted, and has a record of you stopping playback part way through the last time it was inserted, that's when the player can offer to resume playback at the part-way point.
None of this takes any calculation / processing / time on the players part, and only a tiny amount of memory to store.
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