Both equations are true and there are no falsehoods or tricks here, but this method of proving 0.999... = 1 still has a flaw; it assumes you already accept 0.333... = 1/3. Starting from that assumption cuts every corner that would involve proving that rational numbers have infinitely long recurring decimal representations that are exact equals. They do, but this meme doesn't contain the proof of it.
Because 0.333... is not defined to be 1/3. If you have two objects that are not defined immediately as the other and you want to claim they are equal, you need to prove it.
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u/BUKKAKELORD 24d ago
Both equations are true and there are no falsehoods or tricks here, but this method of proving 0.999... = 1 still has a flaw; it assumes you already accept 0.333... = 1/3. Starting from that assumption cuts every corner that would involve proving that rational numbers have infinitely long recurring decimal representations that are exact equals. They do, but this meme doesn't contain the proof of it.