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I think technology can keep things going for a long time yet. England's population density is about 380 people per km2. If you got the whole world to that density, the total population would be about 57 billion. To do this, you would need to have essentially unlimited energy resources, to get water to all areas of the globe, and presumably some sort of geo-engineering projects to deal with the various repercussions. But I don't see any actual limits.