This is correct. For example: Let's say the population is P and the net reproduction rate (the number of daughters a woman has in her lifetime) is 0.9. The next

This is correct. For example: Let's say the population is P and the net reproduction rate (the number of daughters a woman has in her lifetime) is 0.9. The next generation would have 0.9P people, the next one would have 0.9², then 0.9³, etc. Even with immortality you would get lim_(i→∞)∑ᵢ0.9ⁱP = 9P. So as long as the net reproduction rate is less than one the population stabilises at a finite number even if everyone is immortal.