Does learning language rules require remembering everything?

A learner observing language examples one-at-a-time must eventually generate only valid new sentences—but with limited memory. This work proves that memoryless generation works for any countable language collection (under mild conditions), using Sperner's theorem to characterize optimal worst-case performance. Crucially, adaptive memory helps more than a simple sliding window, and identifying the exact target rule breaks down with just three language options, though approximate identification always works.