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@tatsumoto That isn't a problem at all unless some genius's have arranged so the economy only functions if the "line goes up" forever.
Oh wait, that has been done, in ignorance of the concept that resources are finite.
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@tatsumoto The last Japanese won't die in only a few decades, considering the current population is a little under 123,540,000 and I reckon at least 100 million of those qualify as "Japanese".
Assuming a average birth rate of 1 child per woman and the replacement rate never returns (it probably will eventually when the is no longer too many people), in >50 years, the population of Japanese will reduce to ~50 million, if that continues, then in another >50 years, the population will be ~25 million, then ~12.5 million, then ~6.25 million, then ~3.1 million then ~1.5 million.
So really it'll take longer than 300 years before there is the risk of the "last Japanese dying".
Humanity is now global and really reproduction is done globally, thus there is pretty much no "country specific bloodlines" anymore.
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@Suiseiseki I sometimes wonder who will populate Japan in a few decades after the last Japanese dies.