You're not wrong, but something can work well enough to still be useful despite falling short of the idea of a proof or any formal definition.
Let's say that 95% of individual humans can pass it and only 2% of bots. For someone maintaining a website, who has to decide between using this system and shutting down their site because of the increased costs, that may very well be good enough
Let's say that 95% of individual humans can pass it and only 2% of bots. For someone maintaining a website, who has to decide between using this system and shutting down their site because of the increased costs, that may very well be good enough