I remember once I asking myself - How many people are there in the future world, like a world in star trek series. And what's the projection of the world population will be in the year of 2500. Using a basic mathematical extrapolation, that with simply 1% of annual population growth rate. (Currently about 1.1%). It will take less than 500 years for the world population growing from 7 billions to 1 trillion, if there is no major event that ends the civilizations.
However it's base on the assumption that everything is perfect, and the technologies in the future will solve the food production problems, and people start moving out of the Earth surface. But if people only stay on the Earth with technologies and industries remained the same as we currently have, then a rough calculation[1] can tell us that the agriculture department can only sustain about 50 billions on Earth (the carrying capacity of Earth under current method). And the world population estimation is about 9 to 11 billions on 2050.
This is a passive view about how the world can not sustain more than certain populations. (ranging from 3 billions to 100 billions). But it's all done on the base that technology will not advanced beyond current capacity. It's clearly not the case. In the beginning of the 20th century before green evolution, people predicted that the world population can not exceeded 3 billions, and we did. And there is no stopping for the development of new techs to produce more food and create more living space. There are numerous imaginations in the sifi world, and even in real world revolution right now to topple the limit. (Like mariculture revolution to create food from the ocean which covers 70% of earth surface).
So What do you think a world in the future that can support 1 trillion people would look like? Will it be a space colonization world that earth import foods from Mars? Or people dig out massive underground space, and making the Earth look like the Caves of Steel, farming microbes to synthesize food? What's your vision of the future?
[1] There are about 15 million kilometer squares of farming land available right not. And 1 km2 can produce about 5,00 to 900 tons of crops annually. And 1 adult need to consume about 200 kg (0.2 tons) of crops annually for the 2,000 Kcal/day basic requirements (everyone is vege, no meat). Put the number in you will get 15,000,000 * (500 ~ 900) / 0.2 = 38 ~ 68 billions, hence an average about 50 billions.