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Scanning thousands of native English clips with synchronized subtitles and exact timestamps.
Pronunciation Guide
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Listen to native speakers pronounce “banach” in real conversational contexts with synchronized timestamps and subtitles.
and somehow ended up with two identical copies.This is exactly what Banach and Tarski did, but with a ball, like our graph, we again have four moves.We can rotate the ball up, down, left or right, and again, our only rule is that we can't immediately reverse a move.