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Listen to native speakers pronounce “liouville” in real conversational contexts with synchronized timestamps and subtitles.
- Oh, great. So it was Liouville who first proved that there are transcendental numbers, and he exhibited a very specific numberthat's now known as the Liouville constant, which is a transcendental number. Cantor also famously proved that there are many, many transcendental numbers. In fact, it follows from hisargument on the uncountability of the real numbers that there are uncountably many transcendental numbers. So most real numbers are transcendental.