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Proofs of the uncountability of the reals
Recently, I learnt in my evaluation class the proof of the uncountability of the reals by way of the Nested Interval Theorem (Wayback Machine). At first, I used to be wrathful to behold a variant proof (because it didn’t employ the diagonal dispute explicitly). However, as time handed, I started to behold that the proof was simply the ancient one veiled underneath fresh terminology. So, until now I consider that any proof of the uncountability of the reals should employ Cantor’s diagonal dispute.
Is my conviction justified?
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