It depends on technology. The current population is not sustainable because we rely on fossil fuels that will run out. And we are raising the temperature of the planet that will eventually cause massive problems.
Daily and even yearly this is sustainable. We could have a population of 10 billion and sustain it for decades. But it is all based on using resources that are not being replaced and will eventually run out.
But it all comes down to energy. If we could get cheap solar power we could large eliminate fossil fuel use, get fresh water by desalinating sea water, grow plants in hyrdoponics in skyscrapers with electric lights, pull carbon out of the air to reduce the greenhouse effect, etc.
We can accomplish amazing things, but we need energy to do it. And fossil fuel as an energy source is not sustainable. Also we use fossil fuels as a source of fertilizer for farming which is not sustainable.
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