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The way the game is set up, you gradually learn all the new Pokemon and moves in each gen by getting exposed to a few in each new section of the game (Route, Cave, Gym, etc).
Couple that with the human mind's amazing capacity to store and retrieve information that's associated with an image, it is entirely plausible for a healthy human mind to memorize every Pokemon out there, up to this point.
Take for example babies. When they're learning how to talk, a lot of parents use flash cards to help them learn words. That word (such as "apple") will then always be associated to that image of an apple. Just simply apply that theory to Pokemon. If you go around calling a yellow rat with electrical powers "Pikachu" eventually, you're going to know to call the thing "Pikachu" just based on a simple image.
I would even go so far as to say that, so long as the formula stays the same, we could probably have 1000+ and still know each and every one's name and type based on appearance alone.
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A better question would be is if it's possible to memorize every pokemon, their national and regional dex numbers, what moves they learn, specifically how they learn it (e.g. what level?), specifically how they evolve (again, like what level?), which game and versions feature them, which locations can they be found in, what egg groups they belong in, which trainers uses them if any, and what their base stats are.
...but it'd still be a yes or no answer, so it's not that much better.
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