system
Given the following post, respond as if you're commenting on Reddit:
human
I don't know how hard this is to answer but... About how many healthy people would need to survive the Apocalypse to repopulate the earth without inbreeding?
gpt
If you survive and just a fraction of humanity remains, inbreeding should be the least of your concerns.

Bottlenecked populations will go through inbreeding depression, but then will generally recover over geologic time.

An effective population size of 100 is pretty good for avoiding the worst effects, 1000 is quite good, and 10000 is probably fine. Of course, this depends upon things like how closely the individuals are related to begin with and relative male/female ratios.